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 |
|---|---|
| 22 and 63 | 1386 |
| 123 and 191 | 23493 |
| 185 and 60 | 2220 |
| 164 and 199 | 32636 |
| 181 and 199 | 36019 |