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Least Common Multiple (LCM) of 65 and 116

The least common multiple (LCM) of 65 and 116 is 7540.

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 116?

First, calculate the GCD of 65 and 116 using the Euclidean algorithm. Then use the formula above to find the LCM.

Step-by-Step GCD Calculation

StepCalculation
1 65 ÷ 116 = 0 remainder 65
2 116 ÷ 65 = 1 remainder 51
3 65 ÷ 51 = 1 remainder 14
4 51 ÷ 14 = 3 remainder 9
5 14 ÷ 9 = 1 remainder 5
6 9 ÷ 5 = 1 remainder 4
7 5 ÷ 4 = 1 remainder 1
8 4 ÷ 1 = 4 remainder 0

Examples of LCM Calculations

NumbersLCM
91 and 26182
73 and 967008
141 and 17524675
99 and 963168
128 and 441408

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