Least Common Multiple (LCM) of 101 and 178
The least common multiple (LCM) of 101 and 178 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 101 and 178?
First, calculate the GCD of 101 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 178 = 0 remainder 101 |
| 2 | 178 ÷ 101 = 1 remainder 77 |
| 3 | 101 ÷ 77 = 1 remainder 24 |
| 4 | 77 ÷ 24 = 3 remainder 5 |
| 5 | 24 ÷ 5 = 4 remainder 4 |
| 6 | 5 ÷ 4 = 1 remainder 1 |
| 7 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 30 and 198 | 990 |
| 148 and 42 | 3108 |
| 27 and 166 | 4482 |
| 92 and 62 | 2852 |
| 142 and 174 | 12354 |