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 |
|---|---|
| 178 and 178 | 178 |
| 190 and 19 | 190 |
| 122 and 196 | 11956 |
| 163 and 13 | 2119 |
| 39 and 173 | 6747 |