Least Common Multiple (LCM) of 167 and 178
The least common multiple (LCM) of 167 and 178 is 29726.
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 167 and 178?
First, calculate the GCD of 167 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 167 ÷ 178 = 0 remainder 167 |
| 2 | 178 ÷ 167 = 1 remainder 11 |
| 3 | 167 ÷ 11 = 15 remainder 2 |
| 4 | 11 ÷ 2 = 5 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 45 and 101 | 4545 |
| 153 and 58 | 8874 |
| 123 and 81 | 3321 |
| 194 and 61 | 11834 |
| 65 and 179 | 11635 |