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Least Common Multiple (LCM) of 105 and 199

The least common multiple (LCM) of 105 and 199 is 20895.

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 199?

First, calculate the GCD of 105 and 199 using the Euclidean algorithm. Then use the formula above to find the LCM.

Step-by-Step GCD Calculation

StepCalculation
1 105 ÷ 199 = 0 remainder 105
2 199 ÷ 105 = 1 remainder 94
3 105 ÷ 94 = 1 remainder 11
4 94 ÷ 11 = 8 remainder 6
5 11 ÷ 6 = 1 remainder 5
6 6 ÷ 5 = 1 remainder 1
7 5 ÷ 1 = 5 remainder 0

Examples of LCM Calculations

NumbersLCM
154 and 201540
185 and 14927565
149 and 14321307
150 and 19729550
91 and 771001

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