Least Common Multiple (LCM) of 120 and 64
The least common multiple (LCM) of 120 and 64 is 960.
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 64?
First, calculate the GCD of 120 and 64 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 64 = 1 remainder 56 |
| 2 | 64 ÷ 56 = 1 remainder 8 |
| 3 | 56 ÷ 8 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 25 and 63 | 1575 |
| 49 and 172 | 8428 |
| 55 and 191 | 10505 |
| 18 and 125 | 2250 |
| 105 and 13 | 1365 |