Least Common Multiple (LCM) of 102 and 174
The least common multiple (LCM) of 102 and 174 is 2958.
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 102 and 174?
First, calculate the GCD of 102 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 102 ÷ 174 = 0 remainder 102 |
| 2 | 174 ÷ 102 = 1 remainder 72 |
| 3 | 102 ÷ 72 = 1 remainder 30 |
| 4 | 72 ÷ 30 = 2 remainder 12 |
| 5 | 30 ÷ 12 = 2 remainder 6 |
| 6 | 12 ÷ 6 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 18 | 90 |
| 147 and 189 | 1323 |
| 178 and 69 | 12282 |
| 123 and 166 | 20418 |
| 88 and 98 | 4312 |