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 |
|---|---|
| 127 and 199 | 25273 |
| 29 and 61 | 1769 |
| 162 and 141 | 7614 |
| 18 and 111 | 666 |
| 112 and 137 | 15344 |