Least Common Multiple (LCM) of 21 and 79
The least common multiple (LCM) of 21 and 79 is 1659.
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 79?
First, calculate the GCD of 21 and 79 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 79 = 0 remainder 21 |
| 2 | 79 ÷ 21 = 3 remainder 16 |
| 3 | 21 ÷ 16 = 1 remainder 5 |
| 4 | 16 ÷ 5 = 3 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 119 | 18683 |
| 168 and 146 | 12264 |
| 123 and 50 | 6150 |
| 82 and 25 | 2050 |
| 136 and 102 | 408 |