Least Common Multiple (LCM) of 63 and 117
The least common multiple (LCM) of 63 and 117 is 819.
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 63 and 117?
First, calculate the GCD of 63 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 63 ÷ 117 = 0 remainder 63 |
| 2 | 117 ÷ 63 = 1 remainder 54 |
| 3 | 63 ÷ 54 = 1 remainder 9 |
| 4 | 54 ÷ 9 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 63 | 756 |
| 102 and 115 | 11730 |
| 34 and 139 | 4726 |
| 45 and 113 | 5085 |
| 32 and 153 | 4896 |