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Least Common Multiple (LCM) of 21 and 67

The least common multiple (LCM) of 21 and 67 is 1407.

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 21 and 67?

First, calculate the GCD of 21 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.

Step-by-Step GCD Calculation

StepCalculation
1 21 ÷ 67 = 0 remainder 21
2 67 ÷ 21 = 3 remainder 4
3 21 ÷ 4 = 5 remainder 1
4 4 ÷ 1 = 4 remainder 0

Examples of LCM Calculations

NumbersLCM
152 and 17726904
60 and 1842760
155 and 1103410
158 and 579006
122 and 1187198

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