Least Common Multiple (LCM) of 125 and 72
The least common multiple (LCM) of 125 and 72 is 9000.
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 125 and 72?
First, calculate the GCD of 125 and 72 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 72 = 1 remainder 53 |
| 2 | 72 ÷ 53 = 1 remainder 19 |
| 3 | 53 ÷ 19 = 2 remainder 15 |
| 4 | 19 ÷ 15 = 1 remainder 4 |
| 5 | 15 ÷ 4 = 3 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 156 and 146 | 11388 |
| 90 and 195 | 1170 |
| 32 and 68 | 544 |
| 181 and 51 | 9231 |
| 103 and 77 | 7931 |