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Least Common Multiple (LCM) of 105 and 174

The least common multiple (LCM) of 105 and 174 is 6090.

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 105 and 174?

First, calculate the GCD of 105 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.

Step-by-Step GCD Calculation

StepCalculation
1 105 ÷ 174 = 0 remainder 105
2 174 ÷ 105 = 1 remainder 69
3 105 ÷ 69 = 1 remainder 36
4 69 ÷ 36 = 1 remainder 33
5 36 ÷ 33 = 1 remainder 3
6 33 ÷ 3 = 11 remainder 0

Examples of LCM Calculations

NumbersLCM
34 and 1635542
150 and 20300
34 and 1963332
86 and 1446192
95 and 19318335

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