Least Common Multiple (LCM) of 77 and 174
The least common multiple (LCM) of 77 and 174 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 77 and 174?
First, calculate the GCD of 77 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 77 ÷ 174 = 0 remainder 77 |
| 2 | 174 ÷ 77 = 2 remainder 20 |
| 3 | 77 ÷ 20 = 3 remainder 17 |
| 4 | 20 ÷ 17 = 1 remainder 3 |
| 5 | 17 ÷ 3 = 5 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 106 and 170 | 9010 |
| 58 and 24 | 696 |
| 189 and 25 | 4725 |
| 135 and 141 | 6345 |
| 22 and 55 | 110 |