Least Common Multiple (LCM) of 120 and 63
The least common multiple (LCM) of 120 and 63 is 2520.
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 63?
First, calculate the GCD of 120 and 63 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 63 = 1 remainder 57 |
| 2 | 63 ÷ 57 = 1 remainder 6 |
| 3 | 57 ÷ 6 = 9 remainder 3 |
| 4 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 54 and 102 | 918 |
| 149 and 141 | 21009 |
| 77 and 57 | 4389 |
| 161 and 33 | 5313 |
| 136 and 108 | 3672 |