Least Common Multiple (LCM) of 144 and 172
The least common multiple (LCM) of 144 and 172 is 6192.
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 172?
First, calculate the GCD of 144 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 144 ÷ 172 = 0 remainder 144 |
| 2 | 172 ÷ 144 = 1 remainder 28 |
| 3 | 144 ÷ 28 = 5 remainder 4 |
| 4 | 28 ÷ 4 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 117 and 66 | 2574 |
| 99 and 16 | 1584 |
| 56 and 13 | 728 |
| 79 and 122 | 9638 |
| 123 and 193 | 23739 |