Least Common Multiple (LCM) of 172 and 102
The least common multiple (LCM) of 172 and 102 is 8772.
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 172 and 102?
First, calculate the GCD of 172 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 102 = 1 remainder 70 |
| 2 | 102 ÷ 70 = 1 remainder 32 |
| 3 | 70 ÷ 32 = 2 remainder 6 |
| 4 | 32 ÷ 6 = 5 remainder 2 |
| 5 | 6 ÷ 2 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 52 and 132 | 1716 |
| 185 and 77 | 14245 |
| 104 and 70 | 3640 |
| 109 and 99 | 10791 |
| 180 and 135 | 540 |