Least Common Multiple (LCM) of 126 and 72
The least common multiple (LCM) of 126 and 72 is 504.
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 126 and 72?
First, calculate the GCD of 126 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 126 ÷ 72 = 1 remainder 54 |
| 2 | 72 ÷ 54 = 1 remainder 18 |
| 3 | 54 ÷ 18 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 13 and 198 | 2574 |
| 189 and 119 | 3213 |
| 43 and 129 | 129 |
| 59 and 60 | 3540 |
| 179 and 175 | 31325 |