Least Common Multiple (LCM) of 67 and 174
The least common multiple (LCM) of 67 and 174 is 11658.
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 67 and 174?
First, calculate the GCD of 67 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 67 ÷ 174 = 0 remainder 67 |
| 2 | 174 ÷ 67 = 2 remainder 40 |
| 3 | 67 ÷ 40 = 1 remainder 27 |
| 4 | 40 ÷ 27 = 1 remainder 13 |
| 5 | 27 ÷ 13 = 2 remainder 1 |
| 6 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 19 and 76 | 76 |
| 28 and 18 | 252 |
| 98 and 71 | 6958 |
| 46 and 70 | 1610 |
| 16 and 28 | 112 |