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Least Common Multiple (LCM) of 180 and 109

The least common multiple (LCM) of 180 and 109 is 19620.

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 180 and 109?

First, calculate the GCD of 180 and 109 using the Euclidean algorithm. Then use the formula above to find the LCM.

Step-by-Step GCD Calculation

StepCalculation
1 180 ÷ 109 = 1 remainder 71
2 109 ÷ 71 = 1 remainder 38
3 71 ÷ 38 = 1 remainder 33
4 38 ÷ 33 = 1 remainder 5
5 33 ÷ 5 = 6 remainder 3
6 5 ÷ 3 = 1 remainder 2
7 3 ÷ 2 = 1 remainder 1
8 2 ÷ 1 = 2 remainder 0

Examples of LCM Calculations

NumbersLCM
191 and 15329223
195 and 11322035
142 and 1087668
145 and 314495
154 and 15523870

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