Least Common Multiple (LCM) of 120 and 25
The least common multiple (LCM) of 120 and 25 is 600.
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 120 and 25?
First, calculate the GCD of 120 and 25 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 25 = 4 remainder 20 |
| 2 | 25 ÷ 20 = 1 remainder 5 |
| 3 | 20 ÷ 5 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 176 | 3696 |
| 160 and 120 | 480 |
| 50 and 157 | 7850 |
| 185 and 167 | 30895 |
| 45 and 161 | 7245 |