Least Common Multiple (LCM) of 120 and 84
The least common multiple (LCM) of 120 and 84 is 840.
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 84?
First, calculate the GCD of 120 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 84 = 1 remainder 36 |
| 2 | 84 ÷ 36 = 2 remainder 12 |
| 3 | 36 ÷ 12 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 164 | 4428 |
| 193 and 38 | 7334 |
| 140 and 86 | 6020 |
| 22 and 199 | 4378 |
| 53 and 50 | 2650 |