Least Common Multiple (LCM) of 107 and 120
The least common multiple (LCM) of 107 and 120 is 12840.
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 107 and 120?
First, calculate the GCD of 107 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 107 ÷ 120 = 0 remainder 107 |
| 2 | 120 ÷ 107 = 1 remainder 13 |
| 3 | 107 ÷ 13 = 8 remainder 3 |
| 4 | 13 ÷ 3 = 4 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 112 and 96 | 672 |
| 53 and 66 | 3498 |
| 17 and 52 | 884 |
| 104 and 138 | 7176 |
| 72 and 77 | 5544 |