Least Common Multiple (LCM) of 144 and 21
The least common multiple (LCM) of 144 and 21 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 144 and 21?
First, calculate the GCD of 144 and 21 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 21 = 6 remainder 18 |
| 2 | 21 ÷ 18 = 1 remainder 3 |
| 3 | 18 ÷ 3 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 182 and 39 | 546 |
| 187 and 97 | 18139 |
| 83 and 132 | 10956 |
| 32 and 165 | 5280 |
| 110 and 40 | 440 |