Least Common Multiple (LCM) of 178 and 99
The least common multiple (LCM) of 178 and 99 is 17622.
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 99?
First, calculate the GCD of 178 and 99 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 99 = 1 remainder 79 |
| 2 | 99 ÷ 79 = 1 remainder 20 |
| 3 | 79 ÷ 20 = 3 remainder 19 |
| 4 | 20 ÷ 19 = 1 remainder 1 |
| 5 | 19 ÷ 1 = 19 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 199 | 21094 |
| 152 and 161 | 24472 |
| 180 and 144 | 720 |
| 198 and 187 | 3366 |
| 134 and 131 | 17554 |