Least Common Multiple (LCM) of 174 and 65
The least common multiple (LCM) of 174 and 65 is 11310.
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 65?
First, calculate the GCD of 174 and 65 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 65 = 2 remainder 44 |
| 2 | 65 ÷ 44 = 1 remainder 21 |
| 3 | 44 ÷ 21 = 2 remainder 2 |
| 4 | 21 ÷ 2 = 10 remainder 1 |
| 5 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 42 and 186 | 1302 |
| 83 and 106 | 8798 |
| 141 and 57 | 2679 |
| 175 and 115 | 4025 |
| 135 and 12 | 540 |