Least Common Multiple (LCM) of 60 and 126
The least common multiple (LCM) of 60 and 126 is 1260.
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 60 and 126?
First, calculate the GCD of 60 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 60 ÷ 126 = 0 remainder 60 |
| 2 | 126 ÷ 60 = 2 remainder 6 |
| 3 | 60 ÷ 6 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 129 | 13803 |
| 112 and 75 | 8400 |
| 20 and 155 | 620 |
| 64 and 84 | 1344 |
| 15 and 144 | 720 |