Least Common Multiple (LCM) of 66 and 174
The least common multiple (LCM) of 66 and 174 is 1914.
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 66 and 174?
First, calculate the GCD of 66 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 66 ÷ 174 = 0 remainder 66 |
| 2 | 174 ÷ 66 = 2 remainder 42 |
| 3 | 66 ÷ 42 = 1 remainder 24 |
| 4 | 42 ÷ 24 = 1 remainder 18 |
| 5 | 24 ÷ 18 = 1 remainder 6 |
| 6 | 18 ÷ 6 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 168 and 115 | 19320 |
| 120 and 92 | 2760 |
| 31 and 54 | 1674 |
| 99 and 45 | 495 |
| 62 and 17 | 1054 |