Least Common Multiple (LCM) of 117 and 54
The least common multiple (LCM) of 117 and 54 is 702.
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 117 and 54?
First, calculate the GCD of 117 and 54 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 54 = 2 remainder 9 |
| 2 | 54 ÷ 9 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 67 and 67 | 67 |
| 144 and 119 | 17136 |
| 157 and 164 | 25748 |
| 178 and 17 | 3026 |
| 106 and 129 | 13674 |