Least Common Multiple (LCM) of 44 and 117
The least common multiple (LCM) of 44 and 117 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 44 and 117?
First, calculate the GCD of 44 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 44 ÷ 117 = 0 remainder 44 |
| 2 | 117 ÷ 44 = 2 remainder 29 |
| 3 | 44 ÷ 29 = 1 remainder 15 |
| 4 | 29 ÷ 15 = 1 remainder 14 |
| 5 | 15 ÷ 14 = 1 remainder 1 |
| 6 | 14 ÷ 1 = 14 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 126 and 20 | 1260 |
| 13 and 109 | 1417 |
| 46 and 22 | 506 |
| 151 and 18 | 2718 |
| 20 and 26 | 260 |