LCM of 50 and 100 is the smallest number among all common multiples of 50 and 100. The first few multiples of 50 and 100 are (50, 100, 150, 200, 250, 300, 350, . . . ) and (100, 200, 300, 400, 500, 600, . . . ) respectively. There are 3 commonly used methods to find LCM of 50 and 100 - by division method, by prime factorization, and by listing multiples.
What is the LCM of 50 and 100?
Answer: LCM of 50 and 100 is 100.
Explanation:
The LCM of two non-zero integers, x(50) and y(100), is the smallest positive integer m(100) that is divisible by both x(50) and y(100) without any remainder.
Methods to Find LCM of 50 and 100
The methods to find the LCM of 50 and 100 are explained below.
By Division MethodBy Listing MultiplesBy Prime Factorization MethodLCM of 50 and 100 by Division Method
To calculate the LCM of 50 and 100 by the division method, we will divide the numbers(50, 100) by their prime factors (preferably common). The product of these divisors gives the LCM of 50 and 100.
Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 50 and 100. Write this prime number(2) on the left of the given numbers(50 and 100), separated as per the ladder arrangement.Step 2: If any of the given numbers (50, 100) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.Step 3: Continue the steps until only 1s are left in the last row.
The LCM of 50 and 100 is the product of all prime numbers on the left, i.e. LCM(50, 100) by division method = 2 × 2 × 5 × 5 = 100.
LCM of 50 and 100 by Listing Multiples
To calculate the LCM of 50 and 100 by listing out the common multiples, we can follow the given below steps:
Step 1: List a few multiples of 50 (50, 100, 150, 200, 250, 300, 350, . . . ) and 100 (100, 200, 300, 400, 500, 600, . . . . )Step 2: The common multiples from the multiples of 50 and 100 are 100, 200, . . .Step 3: The smallest common multiple of 50 and 100 is 100.
∴ The least common multiple of 50 and 100 = 100.
LCM of 50 and 100 by Prime Factorization
Prime factorization of 50 and 100 is (2 × 5 × 5) = 21 × 52 and (2 × 2 × 5 × 5) = 22 × 52 respectively. LCM of 50 and 100 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 22 × 52 = 100.
Hence, the LCM of 50 and 100 by prime factorization is 100.
☛ Also Check:
LCM of 15 and 24 - 120LCM of 6 and 11 - 66LCM of 4 and 5 - 20LCM of 9 and 11 - 99LCM of 10, 15 and 20 - 60LCM of 24 and 42 - 168LCM of 56 and 72 - 504
Read More
LCM of 50 and 100 Examples
Example 2: Find the smallest number that is divisible by 50 and 100 exactly.
Solution:
The smallest number that is divisible by 50 and 100 exactly is their LCM.
Answers & Comments
NameRelationLength OSMSH1456034882.1kmSH24560486107.9kmSH34560754269.7kmSH44560850171.7km
Explanation:
The relation between GCF and LCM of 50 and 100 is given as,
LCM(50, 100) × GCF(50, 100) = Product of 50, 100
Prime factorization of 50 and 100 is given as, 50 = (2 × 5 × 5) = 21 × 52 and 100 = (2 × 2 × 5 × 5) = 22 × 52
LCM(50, 100) = 100
GCF(50, 100) = 50
LHS = LCM(50, 100) × GCF(50, 100) = 100 × 50 = 5000
RHS = Product of 50, 100 = 50 × 100 = 5000
⇒ LHS = RHS = 5000
Hence, verified.
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LCM of 50 and 100
LCM of 50 and 100 is the smallest number among all common multiples of 50 and 100. The first few multiples of 50 and 100 are (50, 100, 150, 200, 250, 300, 350, . . . ) and (100, 200, 300, 400, 500, 600, . . . ) respectively. There are 3 commonly used methods to find LCM of 50 and 100 - by division method, by prime factorization, and by listing multiples.
What is the LCM of 50 and 100?
Answer: LCM of 50 and 100 is 100.
Explanation:
The LCM of two non-zero integers, x(50) and y(100), is the smallest positive integer m(100) that is divisible by both x(50) and y(100) without any remainder.
Methods to Find LCM of 50 and 100
The methods to find the LCM of 50 and 100 are explained below.
By Division MethodBy Listing MultiplesBy Prime Factorization MethodLCM of 50 and 100 by Division Method
To calculate the LCM of 50 and 100 by the division method, we will divide the numbers(50, 100) by their prime factors (preferably common). The product of these divisors gives the LCM of 50 and 100.
Step 1: Find the smallest prime number that is a factor of at least one of the numbers, 50 and 100. Write this prime number(2) on the left of the given numbers(50 and 100), separated as per the ladder arrangement.Step 2: If any of the given numbers (50, 100) is a multiple of 2, divide it by 2 and write the quotient below it. Bring down any number that is not divisible by the prime number.Step 3: Continue the steps until only 1s are left in the last row.
The LCM of 50 and 100 is the product of all prime numbers on the left, i.e. LCM(50, 100) by division method = 2 × 2 × 5 × 5 = 100.
LCM of 50 and 100 by Listing Multiples
To calculate the LCM of 50 and 100 by listing out the common multiples, we can follow the given below steps:
Step 1: List a few multiples of 50 (50, 100, 150, 200, 250, 300, 350, . . . ) and 100 (100, 200, 300, 400, 500, 600, . . . . )Step 2: The common multiples from the multiples of 50 and 100 are 100, 200, . . .Step 3: The smallest common multiple of 50 and 100 is 100.
∴ The least common multiple of 50 and 100 = 100.
LCM of 50 and 100 by Prime Factorization
Prime factorization of 50 and 100 is (2 × 5 × 5) = 21 × 52 and (2 × 2 × 5 × 5) = 22 × 52 respectively. LCM of 50 and 100 can be obtained by multiplying prime factors raised to their respective highest power, i.e. 22 × 52 = 100.
Hence, the LCM of 50 and 100 by prime factorization is 100.
☛ Also Check:
LCM of 15 and 24 - 120LCM of 6 and 11 - 66LCM of 4 and 5 - 20LCM of 9 and 11 - 99LCM of 10, 15 and 20 - 60LCM of 24 and 42 - 168LCM of 56 and 72 - 504
Read More
LCM of 50 and 100 Examples
Example 2: Find the smallest number that is divisible by 50 and 100 exactly.
Solution:
The smallest number that is divisible by 50 and 100 exactly is their LCM.
⇒ Multiples of 50 and 100:
Multiples of 50 = 50, 100, 150, 200, 250, 300, . . . .Multiples of 100 = 100, 200, 300, 400, 500, 600, . . . .
Therefore, the LCM of 50 and 100 is 100.
Example 3: The product of two numbers is 5000. If their GCD is 50, what is their LCM?
Solution:
Given: GCD = 50
product of numbers = 5000
∵ LCM × GCD = product of numbers
⇒ LCM = Product/GCD = 5000/50
Therefore, the LCM is 100.
The probable combination for the given case is LCM(50, 100) = 100.
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FAQs on LCM of 50 and 100
What is the LCM of 50 and 100?
Which of the following is the LCM of 50 and 100? 100, 24, 50, 3
How to Find the LCM of 50 and 100 by Prime Factorization?
If the LCM of 100 and 50 is 100, Find its GCF.
What are the Methods to Find LCM of 50 and 100?
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