Least Common Multiple (LCM) of 178 and 100
The least common multiple (LCM) of 178 and 100 is 8900.
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 178 and 100?
First, calculate the GCD of 178 and 100 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 100 = 1 remainder 78 |
| 2 | 100 ÷ 78 = 1 remainder 22 |
| 3 | 78 ÷ 22 = 3 remainder 12 |
| 4 | 22 ÷ 12 = 1 remainder 10 |
| 5 | 12 ÷ 10 = 1 remainder 2 |
| 6 | 10 ÷ 2 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 121 | 13915 |
| 69 and 75 | 1725 |
| 36 and 16 | 144 |
| 44 and 18 | 396 |
| 141 and 31 | 4371 |