Least Common Multiple (LCM) of 36 and 174
The least common multiple (LCM) of 36 and 174 is 1044.
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 36 and 174?
First, calculate the GCD of 36 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 36 ÷ 174 = 0 remainder 36 |
| 2 | 174 ÷ 36 = 4 remainder 30 |
| 3 | 36 ÷ 30 = 1 remainder 6 |
| 4 | 30 ÷ 6 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 14 and 11 | 154 |
| 34 and 146 | 2482 |
| 68 and 130 | 4420 |
| 53 and 177 | 9381 |
| 111 and 77 | 8547 |