Least Common Multiple (LCM) of 61 and 178
The least common multiple (LCM) of 61 and 178 is 10858.
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 61 and 178?
First, calculate the GCD of 61 and 178 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 178 = 0 remainder 61 |
| 2 | 178 ÷ 61 = 2 remainder 56 |
| 3 | 61 ÷ 56 = 1 remainder 5 |
| 4 | 56 ÷ 5 = 11 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 115 and 122 | 14030 |
| 47 and 185 | 8695 |
| 58 and 14 | 406 |
| 187 and 21 | 3927 |
| 126 and 49 | 882 |