Least Common Multiple (LCM) of 15 and 172
The least common multiple (LCM) of 15 and 172 is 2580.
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 15 and 172?
First, calculate the GCD of 15 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 15 ÷ 172 = 0 remainder 15 |
| 2 | 172 ÷ 15 = 11 remainder 7 |
| 3 | 15 ÷ 7 = 2 remainder 1 |
| 4 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 144 | 7632 |
| 153 and 114 | 5814 |
| 161 and 174 | 28014 |
| 192 and 45 | 2880 |
| 142 and 80 | 5680 |