Least Common Multiple (LCM) of 117 and 66
The least common multiple (LCM) of 117 and 66 is 2574.
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 66?
First, calculate the GCD of 117 and 66 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 66 = 1 remainder 51 |
| 2 | 66 ÷ 51 = 1 remainder 15 |
| 3 | 51 ÷ 15 = 3 remainder 6 |
| 4 | 15 ÷ 6 = 2 remainder 3 |
| 5 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 125 | 22250 |
| 192 and 150 | 4800 |
| 64 and 175 | 11200 |
| 160 and 199 | 31840 |
| 16 and 91 | 1456 |