Least Common Multiple (LCM) of 108 and 179
The least common multiple (LCM) of 108 and 179 is 19332.
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 179?
First, calculate the GCD of 108 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 108 ÷ 179 = 0 remainder 108 |
| 2 | 179 ÷ 108 = 1 remainder 71 |
| 3 | 108 ÷ 71 = 1 remainder 37 |
| 4 | 71 ÷ 37 = 1 remainder 34 |
| 5 | 37 ÷ 34 = 1 remainder 3 |
| 6 | 34 ÷ 3 = 11 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 135 and 78 | 3510 |
| 152 and 75 | 11400 |
| 174 and 55 | 9570 |
| 153 and 138 | 7038 |
| 126 and 74 | 4662 |