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 |
|---|---|
| 157 and 196 | 30772 |
| 37 and 122 | 4514 |
| 114 and 69 | 2622 |
| 132 and 30 | 660 |
| 52 and 38 | 988 |