Least Common Multiple (LCM) of 176 and 125
The least common multiple (LCM) of 176 and 125 is 22000.
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 176 and 125?
First, calculate the GCD of 176 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 176 ÷ 125 = 1 remainder 51 |
| 2 | 125 ÷ 51 = 2 remainder 23 |
| 3 | 51 ÷ 23 = 2 remainder 5 |
| 4 | 23 ÷ 5 = 4 remainder 3 |
| 5 | 5 ÷ 3 = 1 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 156 | 5460 |
| 63 and 88 | 5544 |
| 12 and 135 | 540 |
| 58 and 107 | 6206 |
| 81 and 82 | 6642 |