Least Common Multiple (LCM) of 125 and 70
The least common multiple (LCM) of 125 and 70 is 1750.
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 70?
First, calculate the GCD of 125 and 70 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 70 = 1 remainder 55 |
| 2 | 70 ÷ 55 = 1 remainder 15 |
| 3 | 55 ÷ 15 = 3 remainder 10 |
| 4 | 15 ÷ 10 = 1 remainder 5 |
| 5 | 10 ÷ 5 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 97 | 4365 |
| 115 and 87 | 10005 |
| 129 and 11 | 1419 |
| 54 and 24 | 216 |
| 45 and 56 | 2520 |