Least Common Multiple (LCM) of 117 and 18
The least common multiple (LCM) of 117 and 18 is 234.
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 18?
First, calculate the GCD of 117 and 18 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 18 = 6 remainder 9 |
| 2 | 18 ÷ 9 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 109 and 72 | 7848 |
| 43 and 57 | 2451 |
| 15 and 52 | 780 |
| 115 and 36 | 4140 |
| 102 and 80 | 4080 |