Least Common Multiple (LCM) of 117 and 64
The least common multiple (LCM) of 117 and 64 is 7488.
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 64?
First, calculate the GCD of 117 and 64 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 64 = 1 remainder 53 |
| 2 | 64 ÷ 53 = 1 remainder 11 |
| 3 | 53 ÷ 11 = 4 remainder 9 |
| 4 | 11 ÷ 9 = 1 remainder 2 |
| 5 | 9 ÷ 2 = 4 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 173 and 129 | 22317 |
| 15 and 93 | 465 |
| 103 and 188 | 19364 |
| 51 and 145 | 7395 |
| 145 and 114 | 16530 |