Least Common Multiple (LCM) of 108 and 176
The least common multiple (LCM) of 108 and 176 is 4752.
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 108 and 176?
First, calculate the GCD of 108 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 176 = 0 remainder 108 |
| 2 | 176 ÷ 108 = 1 remainder 68 |
| 3 | 108 ÷ 68 = 1 remainder 40 |
| 4 | 68 ÷ 40 = 1 remainder 28 |
| 5 | 40 ÷ 28 = 1 remainder 12 |
| 6 | 28 ÷ 12 = 2 remainder 4 |
| 7 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 36 and 31 | 1116 |
| 193 and 107 | 20651 |
| 75 and 145 | 2175 |
| 69 and 144 | 3312 |
| 55 and 72 | 3960 |