Least Common Multiple (LCM) of 120 and 126
The least common multiple (LCM) of 120 and 126 is 2520.
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 120 and 126?
First, calculate the GCD of 120 and 126 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 126 = 0 remainder 120 |
| 2 | 126 ÷ 120 = 1 remainder 6 |
| 3 | 120 ÷ 6 = 20 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 16 | 1296 |
| 122 and 162 | 9882 |
| 53 and 39 | 2067 |
| 153 and 31 | 4743 |
| 75 and 33 | 825 |