Least Common Multiple (LCM) of 21 and 133
The least common multiple (LCM) of 21 and 133 is 399.
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 133?
First, calculate the GCD of 21 and 133 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 133 = 0 remainder 21 |
| 2 | 133 ÷ 21 = 6 remainder 7 |
| 3 | 21 ÷ 7 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 108 and 183 | 6588 |
| 25 and 115 | 575 |
| 173 and 141 | 24393 |
| 53 and 62 | 3286 |
| 161 and 46 | 322 |