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Least Common Multiple (LCM) of 19 and 67

The least common multiple (LCM) of 19 and 67 is 1273.

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 19 and 67?

First, calculate the GCD of 19 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.

Step-by-Step GCD Calculation

StepCalculation
1 19 ÷ 67 = 0 remainder 19
2 67 ÷ 19 = 3 remainder 10
3 19 ÷ 10 = 1 remainder 9
4 10 ÷ 9 = 1 remainder 1
5 9 ÷ 1 = 9 remainder 0

Examples of LCM Calculations

NumbersLCM
61 and 18911529
115 and 14216330
99 and 12712573
78 and 715538
93 and 18817484

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