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Least Common Multiple (LCM) of 192 and 105

The least common multiple (LCM) of 192 and 105 is 6720.

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 192 and 105?

First, calculate the GCD of 192 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.

Step-by-Step GCD Calculation

StepCalculation
1 192 ÷ 105 = 1 remainder 87
2 105 ÷ 87 = 1 remainder 18
3 87 ÷ 18 = 4 remainder 15
4 18 ÷ 15 = 1 remainder 3
5 15 ÷ 3 = 5 remainder 0

Examples of LCM Calculations

NumbersLCM
96 and 21672
82 and 963936
169 and 19733293
116 and 15317748
111 and 13414874

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