Least Common Multiple (LCM) of 100 and 172
The least common multiple (LCM) of 100 and 172 is 4300.
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 100 and 172?
First, calculate the GCD of 100 and 172 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 172 = 0 remainder 100 |
| 2 | 172 ÷ 100 = 1 remainder 72 |
| 3 | 100 ÷ 72 = 1 remainder 28 |
| 4 | 72 ÷ 28 = 2 remainder 16 |
| 5 | 28 ÷ 16 = 1 remainder 12 |
| 6 | 16 ÷ 12 = 1 remainder 4 |
| 7 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 39 and 180 | 2340 |
| 32 and 148 | 1184 |
| 81 and 19 | 1539 |
| 195 and 189 | 12285 |
| 66 and 49 | 3234 |