Least Common Multiple (LCM) of 178 and 102
The least common multiple (LCM) of 178 and 102 is 9078.
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 102?
First, calculate the GCD of 178 and 102 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 102 = 1 remainder 76 |
| 2 | 102 ÷ 76 = 1 remainder 26 |
| 3 | 76 ÷ 26 = 2 remainder 24 |
| 4 | 26 ÷ 24 = 1 remainder 2 |
| 5 | 24 ÷ 2 = 12 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 195 | 6630 |
| 35 and 184 | 6440 |
| 135 and 13 | 1755 |
| 31 and 134 | 4154 |
| 85 and 153 | 765 |