What is the least common multiple of \{120, 124, 165\}?

Iris Vaughan

Iris Vaughan

Answered question

2022-02-03

What is the least common multiple of {120,124,165}?

Answer & Explanation

Justice Jacobson

Justice Jacobson

Beginner2022-02-04Added 17 answers

To find the least common multiple, let's do a ' factorization on these numbers:
120=2×2×2×3×5
124=2×2×31
165=3×5×11
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.
2×2×2×
For 3, the next ', two of the numbers have a 3, so we need 1 also.
2×2×2×3×
We also have two numbers with a 5 each:
2×2×2×3×5×
And there is an 11 and a 31:
2×2×2×3×5×11×31=40,920
120×11×31=40,920
124×2×3×5×11=40,920
165×2×2×2×31=40,920

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