Least Common Multiple (LCM) of 100 and 176
The least common multiple (LCM) of 100 and 176 is 4400.
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 176?
First, calculate the GCD of 100 and 176 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 176 = 0 remainder 100 |
| 2 | 176 ÷ 100 = 1 remainder 76 |
| 3 | 100 ÷ 76 = 1 remainder 24 |
| 4 | 76 ÷ 24 = 3 remainder 4 |
| 5 | 24 ÷ 4 = 6 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 170 | 17170 |
| 29 and 65 | 1885 |
| 123 and 176 | 21648 |
| 97 and 45 | 4365 |
| 120 and 75 | 600 |