Least Common Multiple (LCM) of 178 and 117
The least common multiple (LCM) of 178 and 117 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 178 and 117?
First, calculate the GCD of 178 and 117 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 117 = 1 remainder 61 |
| 2 | 117 ÷ 61 = 1 remainder 56 |
| 3 | 61 ÷ 56 = 1 remainder 5 |
| 4 | 56 ÷ 5 = 11 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 86 and 41 | 3526 |
| 58 and 38 | 1102 |
| 81 and 108 | 324 |
| 29 and 23 | 667 |
| 122 and 196 | 11956 |