Least Common Multiple (LCM) of 84 and 120
The least common multiple (LCM) of 84 and 120 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 84 and 120?
First, calculate the GCD of 84 and 120 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 84 ÷ 120 = 0 remainder 84 |
| 2 | 120 ÷ 84 = 1 remainder 36 |
| 3 | 84 ÷ 36 = 2 remainder 12 |
| 4 | 36 ÷ 12 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 120 | 2280 |
| 111 and 82 | 9102 |
| 117 and 82 | 9594 |
| 157 and 45 | 7065 |
| 129 and 163 | 21027 |