Least Common Multiple (LCM) of 21 and 132
The least common multiple (LCM) of 21 and 132 is 924.
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 132?
First, calculate the GCD of 21 and 132 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 132 = 0 remainder 21 |
| 2 | 132 ÷ 21 = 6 remainder 6 |
| 3 | 21 ÷ 6 = 3 remainder 3 |
| 4 | 6 ÷ 3 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 153 | 17595 |
| 40 and 190 | 760 |
| 195 and 104 | 1560 |
| 148 and 105 | 15540 |
| 196 and 118 | 11564 |