Least Common Multiple (LCM) of 174 and 117
The least common multiple (LCM) of 174 and 117 is 6786.
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 174 and 117?
First, calculate the GCD of 174 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 117 = 1 remainder 57 |
| 2 | 117 ÷ 57 = 2 remainder 3 |
| 3 | 57 ÷ 3 = 19 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 32 | 352 |
| 88 and 89 | 7832 |
| 65 and 108 | 7020 |
| 66 and 96 | 1056 |
| 138 and 176 | 12144 |