Least Common Multiple (LCM) of 178 and 104
The least common multiple (LCM) of 178 and 104 is 9256.
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 104?
First, calculate the GCD of 178 and 104 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 104 = 1 remainder 74 |
| 2 | 104 ÷ 74 = 1 remainder 30 |
| 3 | 74 ÷ 30 = 2 remainder 14 |
| 4 | 30 ÷ 14 = 2 remainder 2 |
| 5 | 14 ÷ 2 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 101 and 45 | 4545 |
| 35 and 137 | 4795 |
| 73 and 178 | 12994 |
| 142 and 11 | 1562 |
| 129 and 160 | 20640 |