Least Common Multiple (LCM) of 101 and 172
The least common multiple (LCM) of 101 and 172 is 17372.
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 101 and 172?
First, calculate the GCD of 101 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 172 = 0 remainder 101 |
| 2 | 172 ÷ 101 = 1 remainder 71 |
| 3 | 101 ÷ 71 = 1 remainder 30 |
| 4 | 71 ÷ 30 = 2 remainder 11 |
| 5 | 30 ÷ 11 = 2 remainder 8 |
| 6 | 11 ÷ 8 = 1 remainder 3 |
| 7 | 8 ÷ 3 = 2 remainder 2 |
| 8 | 3 ÷ 2 = 1 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 173 and 68 | 11764 |
| 74 and 17 | 1258 |
| 65 and 165 | 2145 |
| 38 and 77 | 2926 |
| 191 and 159 | 30369 |