Least Common Multiple (LCM) of 144 and 168
The least common multiple (LCM) of 144 and 168 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 168?
First, calculate the GCD of 144 and 168 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 168 = 0 remainder 144 |
| 2 | 168 ÷ 144 = 1 remainder 24 |
| 3 | 144 ÷ 24 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 12 | 84 |
| 39 and 54 | 702 |
| 157 and 115 | 18055 |
| 155 and 128 | 19840 |
| 29 and 157 | 4553 |