Least Common Multiple (LCM) of 117 and 44
The least common multiple (LCM) of 117 and 44 is 5148.
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 44?
First, calculate the GCD of 117 and 44 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 44 = 2 remainder 29 |
| 2 | 44 ÷ 29 = 1 remainder 15 |
| 3 | 29 ÷ 15 = 1 remainder 14 |
| 4 | 15 ÷ 14 = 1 remainder 1 |
| 5 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 40 and 50 | 200 |
| 52 and 105 | 5460 |
| 89 and 141 | 12549 |
| 42 and 83 | 3486 |
| 166 and 38 | 3154 |