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Least Common Multiple (LCM) of 67 and 105

The least common multiple (LCM) of 67 and 105 is 7035.

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 67 and 105?

First, calculate the GCD of 67 and 105 using the Euclidean algorithm. Then use the formula above to find the LCM.

Step-by-Step GCD Calculation

StepCalculation
1 67 ÷ 105 = 0 remainder 67
2 105 ÷ 67 = 1 remainder 38
3 67 ÷ 38 = 1 remainder 29
4 38 ÷ 29 = 1 remainder 9
5 29 ÷ 9 = 3 remainder 2
6 9 ÷ 2 = 4 remainder 1
7 2 ÷ 1 = 2 remainder 0

Examples of LCM Calculations

NumbersLCM
91 and 1401820
177 and 12221594
184 and 10519320
52 and 1584108
35 and 1501050

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