Least Common Multiple (LCM) of 140 and 179
The least common multiple (LCM) of 140 and 179 is 25060.
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 140 and 179?
First, calculate the GCD of 140 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 140 ÷ 179 = 0 remainder 140 |
| 2 | 179 ÷ 140 = 1 remainder 39 |
| 3 | 140 ÷ 39 = 3 remainder 23 |
| 4 | 39 ÷ 23 = 1 remainder 16 |
| 5 | 23 ÷ 16 = 1 remainder 7 |
| 6 | 16 ÷ 7 = 2 remainder 2 |
| 7 | 7 ÷ 2 = 3 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 84 | 1428 |
| 198 and 15 | 990 |
| 160 and 82 | 6560 |
| 132 and 107 | 14124 |
| 169 and 24 | 4056 |