Expert answers to "What is the least common multiple of {120,124,165}?"

High School
Algebra
Pre-Algebra
Factors and multiples

Iris Vaughan

Answered question

2022-02-03

What is the least common multiple of

{120, 124, 165}

Answer & Explanation

Justice Jacobson

Beginner2022-02-04Added 17 answers

To find the least common multiple, let's do a ' factorization on these numbers:
$120 = 2 \times 2 \times 2 \times 3 \times 5$
$124 = 2 \times 2 \times 31$
$165 = 3 \times 5 \times 11$
To find the lowest common multiple, we take the largest group of 's we can choose from.
For instance, the first ' is 2. The 120 has 3 of them and that is the most that any of our other numbers have. So we need 3 2s.
$2 \times 2 \times 2 \times \dots$
For 3, the next ', two of the numbers have a 3, so we need 1 also.
$2 \times 2 \times 2 \times 3 \times \dots$
We also have two numbers with a 5 each:
$2 \times 2 \times 2 \times 3 \times 5 \times \dots$
And there is an 11 and a 31:
$2 \times 2 \times 2 \times 3 \times 5 \times 11 \times 31 = 40, 920$
$120 \times 11 \times 31 = 40, 920$
$124 \times 2 \times 3 \times 5 \times 11 = 40, 920$
$165 \times 2 \times 2 \times 2 \times 31 = 40, 920$

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