Least Common Multiple (LCM) of 144 and 84
The least common multiple (LCM) of 144 and 84 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 84?
First, calculate the GCD of 144 and 84 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 84 = 1 remainder 60 |
| 2 | 84 ÷ 60 = 1 remainder 24 |
| 3 | 60 ÷ 24 = 2 remainder 12 |
| 4 | 24 ÷ 12 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 90 and 47 | 4230 |
| 176 and 94 | 8272 |
| 152 and 117 | 17784 |
| 170 and 78 | 6630 |
| 35 and 68 | 2380 |