Least Common Multiple (LCM) of 169 and 125
The least common multiple (LCM) of 169 and 125 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 169 and 125?
First, calculate the GCD of 169 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 169 ÷ 125 = 1 remainder 44 |
| 2 | 125 ÷ 44 = 2 remainder 37 |
| 3 | 44 ÷ 37 = 1 remainder 7 |
| 4 | 37 ÷ 7 = 5 remainder 2 |
| 5 | 7 ÷ 2 = 3 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 145 and 106 | 15370 |
| 47 and 111 | 5217 |
| 100 and 135 | 2700 |
| 148 and 24 | 888 |
| 145 and 74 | 10730 |