Least Common Multiple (LCM) of 144 and 30
The least common multiple (LCM) of 144 and 30 is 720.
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 30?
First, calculate the GCD of 144 and 30 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 30 = 4 remainder 24 |
| 2 | 30 ÷ 24 = 1 remainder 6 |
| 3 | 24 ÷ 6 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 157 and 115 | 18055 |
| 89 and 67 | 5963 |
| 72 and 92 | 1656 |
| 112 and 98 | 784 |
| 190 and 73 | 13870 |