Least Common Multiple (LCM) of 118 and 178
The least common multiple (LCM) of 118 and 178 is 10502.
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 118 and 178?
First, calculate the GCD of 118 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 118 ÷ 178 = 0 remainder 118 |
| 2 | 178 ÷ 118 = 1 remainder 60 |
| 3 | 118 ÷ 60 = 1 remainder 58 |
| 4 | 60 ÷ 58 = 1 remainder 2 |
| 5 | 58 ÷ 2 = 29 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 185 | 17760 |
| 134 and 24 | 1608 |
| 110 and 124 | 6820 |
| 112 and 106 | 5936 |
| 69 and 155 | 10695 |