Least Common Multiple (LCM) of 21 and 144
The least common multiple (LCM) of 21 and 144 is 1008.
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 144?
First, calculate the GCD of 21 and 144 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 21 ÷ 144 = 0 remainder 21 |
| 2 | 144 ÷ 21 = 6 remainder 18 |
| 3 | 21 ÷ 18 = 1 remainder 3 |
| 4 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 175 and 55 | 1925 |
| 131 and 146 | 19126 |
| 101 and 177 | 17877 |
| 95 and 109 | 10355 |
| 179 and 58 | 10382 |