Least Common Multiple (LCM) of 71 and 174
The least common multiple (LCM) of 71 and 174 is 12354.
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 71 and 174?
First, calculate the GCD of 71 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 71 ÷ 174 = 0 remainder 71 |
| 2 | 174 ÷ 71 = 2 remainder 32 |
| 3 | 71 ÷ 32 = 2 remainder 7 |
| 4 | 32 ÷ 7 = 4 remainder 4 |
| 5 | 7 ÷ 4 = 1 remainder 3 |
| 6 | 4 ÷ 3 = 1 remainder 1 |
| 7 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 76 and 178 | 6764 |
| 89 and 58 | 5162 |
| 189 and 138 | 8694 |
| 55 and 144 | 7920 |
| 168 and 30 | 840 |