Least Common Multiple (LCM) of 172 and 99
The least common multiple (LCM) of 172 and 99 is 17028.
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 99?
First, calculate the GCD of 172 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 99 = 1 remainder 73 |
| 2 | 99 ÷ 73 = 1 remainder 26 |
| 3 | 73 ÷ 26 = 2 remainder 21 |
| 4 | 26 ÷ 21 = 1 remainder 5 |
| 5 | 21 ÷ 5 = 4 remainder 1 |
| 6 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 147 and 17 | 2499 |
| 56 and 37 | 2072 |
| 112 and 57 | 6384 |
| 102 and 155 | 15810 |
| 23 and 78 | 1794 |