Least Common Multiple (LCM) of 147 and 178
The least common multiple (LCM) of 147 and 178 is 26166.
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 147 and 178?
First, calculate the GCD of 147 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 147 ÷ 178 = 0 remainder 147 |
| 2 | 178 ÷ 147 = 1 remainder 31 |
| 3 | 147 ÷ 31 = 4 remainder 23 |
| 4 | 31 ÷ 23 = 1 remainder 8 |
| 5 | 23 ÷ 8 = 2 remainder 7 |
| 6 | 8 ÷ 7 = 1 remainder 1 |
| 7 | 7 ÷ 1 = 7 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 96 and 42 | 672 |
| 129 and 63 | 2709 |
| 56 and 153 | 8568 |
| 173 and 86 | 14878 |
| 69 and 185 | 12765 |