Least Common Multiple (LCM) of 50 and 179
The least common multiple (LCM) of 50 and 179 is 8950.
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 50 and 179?
First, calculate the GCD of 50 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 50 ÷ 179 = 0 remainder 50 |
| 2 | 179 ÷ 50 = 3 remainder 29 |
| 3 | 50 ÷ 29 = 1 remainder 21 |
| 4 | 29 ÷ 21 = 1 remainder 8 |
| 5 | 21 ÷ 8 = 2 remainder 5 |
| 6 | 8 ÷ 5 = 1 remainder 3 |
| 7 | 5 ÷ 3 = 1 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 17 and 100 | 1700 |
| 157 and 53 | 8321 |
| 64 and 110 | 3520 |
| 160 and 25 | 800 |
| 51 and 86 | 4386 |