Least Common Multiple (LCM) of 32 and 120
The least common multiple (LCM) of 32 and 120 is 480.
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 32 and 120?
First, calculate the GCD of 32 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 32 ÷ 120 = 0 remainder 32 |
| 2 | 120 ÷ 32 = 3 remainder 24 |
| 3 | 32 ÷ 24 = 1 remainder 8 |
| 4 | 24 ÷ 8 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 138 and 113 | 15594 |
| 171 and 96 | 5472 |
| 33 and 55 | 165 |
| 135 and 165 | 1485 |
| 13 and 128 | 1664 |