Least Common Multiple (LCM) of 174 and 77
The least common multiple (LCM) of 174 and 77 is 13398.
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 174 and 77?
First, calculate the GCD of 174 and 77 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 77 = 2 remainder 20 |
| 2 | 77 ÷ 20 = 3 remainder 17 |
| 3 | 20 ÷ 17 = 1 remainder 3 |
| 4 | 17 ÷ 3 = 5 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 119 and 82 | 9758 |
| 14 and 195 | 2730 |
| 108 and 42 | 756 |
| 14 and 128 | 896 |
| 180 and 84 | 1260 |