Least Common Multiple (LCM) of 45 and 117
The least common multiple (LCM) of 45 and 117 is 585.
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 45 and 117?
First, calculate the GCD of 45 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 45 ÷ 117 = 0 remainder 45 |
| 2 | 117 ÷ 45 = 2 remainder 27 |
| 3 | 45 ÷ 27 = 1 remainder 18 |
| 4 | 27 ÷ 18 = 1 remainder 9 |
| 5 | 18 ÷ 9 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 196 and 140 | 980 |
| 170 and 163 | 27710 |
| 86 and 142 | 6106 |
| 109 and 35 | 3815 |
| 200 and 129 | 25800 |