Least Common Multiple (LCM) of 120 and 68
The least common multiple (LCM) of 120 and 68 is 2040.
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 68?
First, calculate the GCD of 120 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 68 = 1 remainder 52 |
| 2 | 68 ÷ 52 = 1 remainder 16 |
| 3 | 52 ÷ 16 = 3 remainder 4 |
| 4 | 16 ÷ 4 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 139 | 2363 |
| 17 and 40 | 680 |
| 26 and 167 | 4342 |
| 108 and 22 | 1188 |
| 108 and 20 | 540 |