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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
127 and 13717399
152 and 181368
27 and 1794833
106 and 683604
119 and 12114399

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