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 |
|---|---|
| 30 and 180 | 180 |
| 103 and 17 | 1751 |
| 157 and 47 | 7379 |
| 48 and 83 | 3984 |
| 22 and 148 | 1628 |