Least Common Multiple (LCM) of 179 and 200
The least common multiple (LCM) of 179 and 200 is 35800.
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 179 and 200?
First, calculate the GCD of 179 and 200 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 179 ÷ 200 = 0 remainder 179 |
| 2 | 200 ÷ 179 = 1 remainder 21 |
| 3 | 179 ÷ 21 = 8 remainder 11 |
| 4 | 21 ÷ 11 = 1 remainder 10 |
| 5 | 11 ÷ 10 = 1 remainder 1 |
| 6 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 199 and 76 | 15124 |
| 85 and 147 | 12495 |
| 14 and 65 | 910 |
| 96 and 116 | 2784 |
| 106 and 186 | 9858 |