Least Common Multiple (LCM) of 144 and 76
The least common multiple (LCM) of 144 and 76 is 2736.
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 76?
First, calculate the GCD of 144 and 76 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 76 = 1 remainder 68 |
| 2 | 76 ÷ 68 = 1 remainder 8 |
| 3 | 68 ÷ 8 = 8 remainder 4 |
| 4 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 12 | 1212 |
| 183 and 115 | 21045 |
| 87 and 169 | 14703 |
| 189 and 103 | 19467 |
| 54 and 191 | 10314 |