Least Common Multiple (LCM) of 117 and 62
The least common multiple (LCM) of 117 and 62 is 7254.
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 62?
First, calculate the GCD of 117 and 62 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 62 = 1 remainder 55 |
| 2 | 62 ÷ 55 = 1 remainder 7 |
| 3 | 55 ÷ 7 = 7 remainder 6 |
| 4 | 7 ÷ 6 = 1 remainder 1 |
| 5 | 6 ÷ 1 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 180 | 180 |
| 89 and 85 | 7565 |
| 61 and 195 | 11895 |
| 59 and 11 | 649 |
| 49 and 33 | 1617 |