Least Common Multiple (LCM) of 172 and 100
The least common multiple (LCM) of 172 and 100 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 172 and 100?
First, calculate the GCD of 172 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 172 ÷ 100 = 1 remainder 72 |
| 2 | 100 ÷ 72 = 1 remainder 28 |
| 3 | 72 ÷ 28 = 2 remainder 16 |
| 4 | 28 ÷ 16 = 1 remainder 12 |
| 5 | 16 ÷ 12 = 1 remainder 4 |
| 6 | 12 ÷ 4 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 122 and 99 | 12078 |
| 124 and 15 | 1860 |
| 33 and 16 | 528 |
| 99 and 145 | 14355 |
| 101 and 29 | 2929 |