Least Common Multiple (LCM) of 117 and 61
The least common multiple (LCM) of 117 and 61 is 7137.
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 61?
First, calculate the GCD of 117 and 61 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 61 = 1 remainder 56 |
| 2 | 61 ÷ 56 = 1 remainder 5 |
| 3 | 56 ÷ 5 = 11 remainder 1 |
| 4 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 11 | 1309 |
| 69 and 23 | 69 |
| 146 and 134 | 9782 |
| 14 and 90 | 630 |
| 18 and 17 | 306 |