Least Common Multiple (LCM) of 65 and 174
The least common multiple (LCM) of 65 and 174 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 65 and 174?
First, calculate the GCD of 65 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 65 ÷ 174 = 0 remainder 65 |
| 2 | 174 ÷ 65 = 2 remainder 44 |
| 3 | 65 ÷ 44 = 1 remainder 21 |
| 4 | 44 ÷ 21 = 2 remainder 2 |
| 5 | 21 ÷ 2 = 10 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 105 | 3360 |
| 191 and 87 | 16617 |
| 192 and 142 | 13632 |
| 114 and 80 | 4560 |
| 46 and 190 | 4370 |