Least Common Multiple (LCM) of 174 and 73
The least common multiple (LCM) of 174 and 73 is 12702.
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 174 and 73?
First, calculate the GCD of 174 and 73 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 174 ÷ 73 = 2 remainder 28 |
| 2 | 73 ÷ 28 = 2 remainder 17 |
| 3 | 28 ÷ 17 = 1 remainder 11 |
| 4 | 17 ÷ 11 = 1 remainder 6 |
| 5 | 11 ÷ 6 = 1 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 154 and 147 | 3234 |
| 176 and 136 | 2992 |
| 137 and 72 | 9864 |
| 195 and 129 | 8385 |
| 117 and 26 | 234 |