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Least Common Multiple (LCM) of 89 and 113

The least common multiple (LCM) of 89 and 113 is 10057.

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 89 and 113?

First, calculate the GCD of 89 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.

Step-by-Step GCD Calculation

StepCalculation
1 89 ÷ 113 = 0 remainder 89
2 113 ÷ 89 = 1 remainder 24
3 89 ÷ 24 = 3 remainder 17
4 24 ÷ 17 = 1 remainder 7
5 17 ÷ 7 = 2 remainder 3
6 7 ÷ 3 = 2 remainder 1
7 3 ÷ 1 = 3 remainder 0

Examples of LCM Calculations

NumbersLCM
181 and 5910679
127 and 19524765
174 and 17931146
159 and 17327507
170 and 15413090

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