Least Common Multiple (LCM) of 125 and 169
The least common multiple (LCM) of 125 and 169 is 21125.
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 169?
First, calculate the GCD of 125 and 169 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 125 ÷ 169 = 0 remainder 125 |
| 2 | 169 ÷ 125 = 1 remainder 44 |
| 3 | 125 ÷ 44 = 2 remainder 37 |
| 4 | 44 ÷ 37 = 1 remainder 7 |
| 5 | 37 ÷ 7 = 5 remainder 2 |
| 6 | 7 ÷ 2 = 3 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 82 | 8938 |
| 126 and 98 | 882 |
| 12 and 189 | 756 |
| 134 and 65 | 8710 |
| 128 and 169 | 21632 |