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Least Common Multiple (LCM) of 189 and 65

The least common multiple (LCM) of 189 and 65 is 12285.

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 189 and 65?

First, calculate the GCD of 189 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.

Step-by-Step GCD Calculation

StepCalculation
1 189 ÷ 65 = 2 remainder 59
2 65 ÷ 59 = 1 remainder 6
3 59 ÷ 6 = 9 remainder 5
4 6 ÷ 5 = 1 remainder 1
5 5 ÷ 1 = 5 remainder 0

Examples of LCM Calculations

NumbersLCM
171 and 1206840
14 and 32224
57 and 744218
25 and 1122800
14 and 50350

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