LEAST COMMON DENOMINATOR (LCM)

SOLVING WORD PROBLEMS INVOLVING LEAST COMMON DENOMINATOR

Problem:

Mrs. Cortez is going to put books in the shelves of 10 and 20. What is the smallest  number of books that Mrs. Cortez can put using the shelves?

Solution:

1.) What is asked in the problem?

Asked:

The smallest number of books can be put in shelves by Mrs. Cortez

2.) What facts are given?

Given:

The given facts are:

• 10 and 20 books
• shelves

3,) How will you solve the problem?

Answer: I will solve the problem by finding the least common multiple of 10 and 20.

For a solution:

You can use this strategy as an optional method:

Strategy #1: LCM Computation

There is a formula for solving Least Common Multiple (LCM). Here it is:

Note: If you cannot see the formula properly, see the image below/above.

Solution:

Step 1: Find the GCF of 10 and 20.

We can use the continuous division to determine the GCF.

• Divide the two numbers by their common factor and then repeat the same process until there is only divisor 1. If the given are even, start with 2.

Note: If you cannot see the computation properly, see the image below/above.          

Since we are using continuous division, multiply all factors that were the divisor in the first side.

• The divisor that would be the factors are 2 and 5.

Therefore, the GCF is 10.

Step 2: Solve for the LCM of 10 and 20.

The GCF are given. Thus, we need to compute using the formula of LCM.

Therefore, 20 is the LCM.

Strategy #2: Prime Factorization

This method is use through giving the factors of the given numbers.

Solution:

Step 1: Give the factors of 10 and 20.

10 = 2 × 5

20 = 2 × 2 × 5

Step 2: Multiply the factors that are common to only one number and commons on both 10 and 20.

• The commons on 10 and 20 are 2 and 5.
• The number that is only common in 10 is 2.

LCM = 2 × 2 × 5

Step 3: Multiply all the factors.

Therefore, the LCM is 20.

4.) What is the answer to the problem?​

Answer:

The final answer is 20.

#BrainliestBunch