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Least Common Multiple (LCM) of 105 and 57

The least common multiple (LCM) of 105 and 57 is 1995.

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 105 and 57?

First, calculate the GCD of 105 and 57 using the Euclidean algorithm. Then use the formula above to find the LCM.

Step-by-Step GCD Calculation

StepCalculation
1 105 ÷ 57 = 1 remainder 48
2 57 ÷ 48 = 1 remainder 9
3 48 ÷ 9 = 5 remainder 3
4 9 ÷ 3 = 3 remainder 0

Examples of LCM Calculations

NumbersLCM
65 and 12780
199 and 16332437
13 and 1612093
132 and 923036
190 and 13926410

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