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Least Common Multiple (LCM) of 65 and 42

The least common multiple (LCM) of 65 and 42 is 2730.

What is the Least Common Multiple (LCM)?

The LCM of two integers is the smallest positive integer that is divisible by both numbers. It is often used to find common denominators and solve problems involving periodic events.

Formula for LCM

The LCM of two numbers can be calculated using their GCD:

LCM(a, b) = |a × b| ÷ GCD(a, b)

How to Calculate the LCM of 65 and 42?

First, calculate the GCD of 65 and 42 using the Euclidean algorithm. Then use the formula above to find the LCM.

Step-by-Step GCD Calculation

StepCalculation
1 65 ÷ 42 = 1 remainder 23
2 42 ÷ 23 = 1 remainder 19
3 23 ÷ 19 = 1 remainder 4
4 19 ÷ 4 = 4 remainder 3
5 4 ÷ 3 = 1 remainder 1
6 3 ÷ 1 = 3 remainder 0

Examples of LCM Calculations

NumbersLCM
33 and 1735709
119 and 647616
34 and 1615474
13 and 831079
42 and 1215082

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