Least Common Multiple (LCM) of 21 and 37
The least common multiple (LCM) of 21 and 37 is 777.
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 37?
First, calculate the GCD of 21 and 37 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 37 = 0 remainder 21 |
| 2 | 37 ÷ 21 = 1 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 |
|---|---|
| 66 and 50 | 1650 |
| 43 and 198 | 8514 |
| 121 and 61 | 7381 |
| 50 and 52 | 1300 |
| 76 and 95 | 380 |