Least Common Multiple (LCM) of 18 and 172
The least common multiple (LCM) of 18 and 172 is 1548.
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 18 and 172?
First, calculate the GCD of 18 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 18 ÷ 172 = 0 remainder 18 |
| 2 | 172 ÷ 18 = 9 remainder 10 |
| 3 | 18 ÷ 10 = 1 remainder 8 |
| 4 | 10 ÷ 8 = 1 remainder 2 |
| 5 | 8 ÷ 2 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 167 and 119 | 19873 |
| 119 and 194 | 23086 |
| 131 and 138 | 18078 |
| 197 and 196 | 38612 |
| 88 and 136 | 1496 |