Least Common Multiple (LCM) of 21 and 18
The least common multiple (LCM) of 21 and 18 is 126.
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 18?
First, calculate the GCD of 21 and 18 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 18 = 1 remainder 3 |
| 2 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 162 and 56 | 4536 |
| 128 and 118 | 7552 |
| 18 and 108 | 108 |
| 89 and 145 | 12905 |
| 83 and 84 | 6972 |