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Least Common Multiple (LCM) of 30 and 84

The least common multiple (LCM) of 30 and 84 is 420.

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 30 and 84?

First, calculate the GCD of 30 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.

Step-by-Step GCD Calculation

StepCalculation
1 30 ÷ 84 = 0 remainder 30
2 84 ÷ 30 = 2 remainder 24
3 30 ÷ 24 = 1 remainder 6
4 24 ÷ 6 = 4 remainder 0

Examples of LCM Calculations

NumbersLCM
137 and 456165
89 and 11610324
147 and 813969
123 and 164492
35 and 1384830

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