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Least Common Multiple (LCM) of 105 and 71

The least common multiple (LCM) of 105 and 71 is 7455.

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 71?

First, calculate the GCD of 105 and 71 using the Euclidean algorithm. Then use the formula above to find the LCM.

Step-by-Step GCD Calculation

StepCalculation
1 105 ÷ 71 = 1 remainder 34
2 71 ÷ 34 = 2 remainder 3
3 34 ÷ 3 = 11 remainder 1
4 3 ÷ 1 = 3 remainder 0

Examples of LCM Calculations

NumbersLCM
177 and 422478
21 and 105105
181 and 13324073
85 and 17614960
199 and 10320497

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