Least Common Multiple (LCM) of 162 and 125
The least common multiple (LCM) of 162 and 125 is 20250.
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 162 and 125?
First, calculate the GCD of 162 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 162 ÷ 125 = 1 remainder 37 |
| 2 | 125 ÷ 37 = 3 remainder 14 |
| 3 | 37 ÷ 14 = 2 remainder 9 |
| 4 | 14 ÷ 9 = 1 remainder 5 |
| 5 | 9 ÷ 5 = 1 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 119 | 714 |
| 19 and 115 | 2185 |
| 94 and 133 | 12502 |
| 61 and 75 | 4575 |
| 178 and 102 | 9078 |