Least Common Multiple (LCM) of 178 and 101
The least common multiple (LCM) of 178 and 101 is 17978.
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 101?
First, calculate the GCD of 178 and 101 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 178 ÷ 101 = 1 remainder 77 |
| 2 | 101 ÷ 77 = 1 remainder 24 |
| 3 | 77 ÷ 24 = 3 remainder 5 |
| 4 | 24 ÷ 5 = 4 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 118 and 11 | 1298 |
| 117 and 67 | 7839 |
| 126 and 48 | 1008 |
| 105 and 195 | 1365 |
| 187 and 38 | 7106 |