Least Common Multiple (LCM) of 144 and 68
The least common multiple (LCM) of 144 and 68 is 2448.
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 68?
First, calculate the GCD of 144 and 68 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 68 = 2 remainder 8 |
| 2 | 68 ÷ 8 = 8 remainder 4 |
| 3 | 8 ÷ 4 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 72 and 103 | 7416 |
| 58 and 126 | 3654 |
| 113 and 10 | 1130 |
| 86 and 135 | 11610 |
| 102 and 112 | 5712 |