Least Common Multiple (LCM) of 120 and 67
The least common multiple (LCM) of 120 and 67 is 8040.
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 67?
First, calculate the GCD of 120 and 67 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 67 = 1 remainder 53 |
| 2 | 67 ÷ 53 = 1 remainder 14 |
| 3 | 53 ÷ 14 = 3 remainder 11 |
| 4 | 14 ÷ 11 = 1 remainder 3 |
| 5 | 11 ÷ 3 = 3 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 107 and 12 | 1284 |
| 11 and 145 | 1595 |
| 25 and 115 | 575 |
| 116 and 157 | 18212 |
| 177 and 195 | 11505 |