Least Common Multiple (LCM) of 42 and 60
The least common multiple (LCM) of 42 and 60 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 42 and 60?
First, calculate the GCD of 42 and 60 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 60 = 0 remainder 42 |
| 2 | 60 ÷ 42 = 1 remainder 18 |
| 3 | 42 ÷ 18 = 2 remainder 6 |
| 4 | 18 ÷ 6 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 65 and 58 | 3770 |
| 110 and 124 | 6820 |
| 123 and 66 | 2706 |
| 139 and 135 | 18765 |
| 175 and 132 | 23100 |