Least Common Multiple (LCM) of 117 and 178
The least common multiple (LCM) of 117 and 178 is 20826.
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 178?
First, calculate the GCD of 117 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 117 ÷ 178 = 0 remainder 117 |
| 2 | 178 ÷ 117 = 1 remainder 61 |
| 3 | 117 ÷ 61 = 1 remainder 56 |
| 4 | 61 ÷ 56 = 1 remainder 5 |
| 5 | 56 ÷ 5 = 11 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 68 and 37 | 2516 |
| 182 and 192 | 17472 |
| 103 and 118 | 12154 |
| 190 and 67 | 12730 |
| 119 and 125 | 14875 |