Least Common Multiple (LCM) of 125 and 106
The least common multiple (LCM) of 125 and 106 is 13250.
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 106?
First, calculate the GCD of 125 and 106 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 106 = 1 remainder 19 |
| 2 | 106 ÷ 19 = 5 remainder 11 |
| 3 | 19 ÷ 11 = 1 remainder 8 |
| 4 | 11 ÷ 8 = 1 remainder 3 |
| 5 | 8 ÷ 3 = 2 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 57 and 129 | 2451 |
| 93 and 126 | 3906 |
| 192 and 108 | 1728 |
| 27 and 185 | 4995 |
| 200 and 174 | 17400 |