Least Common Multiple (LCM) of 42 and 125
The least common multiple (LCM) of 42 and 125 is 5250.
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 42 and 125?
First, calculate the GCD of 42 and 125 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 42 ÷ 125 = 0 remainder 42 |
| 2 | 125 ÷ 42 = 2 remainder 41 |
| 3 | 42 ÷ 41 = 1 remainder 1 |
| 4 | 41 ÷ 1 = 41 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 171 and 105 | 5985 |
| 170 and 118 | 10030 |
| 169 and 50 | 8450 |
| 158 and 37 | 5846 |
| 50 and 150 | 150 |