Least Common Multiple (LCM) of 21 and 179
The least common multiple (LCM) of 21 and 179 is 3759.
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 21 and 179?
First, calculate the GCD of 21 and 179 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 179 = 0 remainder 21 |
| 2 | 179 ÷ 21 = 8 remainder 11 |
| 3 | 21 ÷ 11 = 1 remainder 10 |
| 4 | 11 ÷ 10 = 1 remainder 1 |
| 5 | 10 ÷ 1 = 10 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 71 and 125 | 8875 |
| 107 and 84 | 8988 |
| 99 and 28 | 2772 |
| 35 and 179 | 6265 |
| 75 and 104 | 7800 |