Write the prime factorization of each of them together.
24=2×2×2×336=2×2×3×340=2×2×2×5
If a number is common, take it once in LCM and take the other remaining factors as they are;
LCM=(2×2×2×3)×3×5=360
Hence, LCM of 24, 36 and 40 is 360.
Note: Another method for finding LCM:
In each step, divide the numbers by their common factor. If no common factor exists, multiply all the divisors of each step and the remaining numbers in the last step to get an answer.
2∣∣24,36,40−−−−−−−−
2∣∣12,18,20−−−−−−−−
2∣∣6,9,10−−−−−−
2∣∣3,9,5−−−−−
1,3,5
If a number is not divisible by the divisor used in that step, take it same as it is the further step.
The LCM (Least common multiple) in arithmetic, LCM (a,b) is the least common multiple of two numbers, a and b. And the LCM is the smallest or least positive integer that is divisible by both a and b.
Example:
Consider the two number 8 and 12 and let us write the multiples of two numbers.
Multiples of 8 = 16, 24, 32, 40 ,48, 56……
Multiples of 12 = 24, 36, 48, 60, 72………
From the above list, we can observe that least common multiples of 8 and 12 is 24.
I.e LCM (8, 12) = 24
Given numbers 24,36 and 40
Let us find the prime factorization of the given numbers
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Verified answer
Answer:
ans is c
Step-by-step explanation:
calculate prime factors of 24, 36 and 40.
Prime factorization of 24:
2|24−−−2|12−−−2|6−− 3
24=2×2×2×3=23×3
Prime factorization of 36:
2|36−−−2|18−−−3|9−− 3
36=2×2×3×3=22×32
Prime factorization of 40:
2|40−−−2|20−−−2|10−−− 5
40=2×2×2×5=23×5
Step 2:
Write the prime factorization of each of them together.
24=2×2×2×336=2×2×3×340=2×2×2×5
If a number is common, take it once in LCM and take the other remaining factors as they are;
LCM=(2×2×2×3)×3×5=360
Hence, LCM of 24, 36 and 40 is 360.
Note: Another method for finding LCM:
In each step, divide the numbers by their common factor. If no common factor exists, multiply all the divisors of each step and the remaining numbers in the last step to get an answer.
2∣∣24,36,40−−−−−−−−
2∣∣12,18,20−−−−−−−−
2∣∣6,9,10−−−−−−
2∣∣3,9,5−−−−−
1,3,5
If a number is not divisible by the divisor used in that step, take it same as it is the further step.
LCM=2×2×2×3×3×5=360
Step-by-step explanation:
Answer: LCM of (24, 36, 40) = 360
The LCM (Least common multiple) in arithmetic, LCM (a,b) is the least common multiple of two numbers, a and b. And the LCM is the smallest or least positive integer that is divisible by both a and b.
Example:
Consider the two number 8 and 12 and let us write the multiples of two numbers.
Multiples of 8 = 16, 24, 32, 40 ,48, 56……
Multiples of 12 = 24, 36, 48, 60, 72………
From the above list, we can observe that least common multiples of 8 and 12 is 24.
I.e LCM (8, 12) = 24
Given numbers 24,36 and 40
Let us find the prime factorization of the given numbers
24 = 2 × 3 × 2 × 2
36 = 2 × 3 × 3 × 2
40 = 2 × 2 × 2 × 5
LCM of (24, 36, 40) =2 × 3 × 2 × 2 × 3 × 5
LCM of (24, 36, 40) = 360
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