Least Common Multiple (LCM) of 21 and 76
The least common multiple (LCM) of 21 and 76 is 1596.
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 76?
First, calculate the GCD of 21 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 76 = 0 remainder 21 |
| 2 | 76 ÷ 21 = 3 remainder 13 |
| 3 | 21 ÷ 13 = 1 remainder 8 |
| 4 | 13 ÷ 8 = 1 remainder 5 |
| 5 | 8 ÷ 5 = 1 remainder 3 |
| 6 | 5 ÷ 3 = 1 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 62 and 23 | 1426 |
| 188 and 20 | 940 |
| 63 and 72 | 504 |
| 167 and 193 | 32231 |
| 175 and 150 | 1050 |