Least Common Multiple (LCM) of 146 and 174
The least common multiple (LCM) of 146 and 174 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 146 and 174?
First, calculate the GCD of 146 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 146 ÷ 174 = 0 remainder 146 |
| 2 | 174 ÷ 146 = 1 remainder 28 |
| 3 | 146 ÷ 28 = 5 remainder 6 |
| 4 | 28 ÷ 6 = 4 remainder 4 |
| 5 | 6 ÷ 4 = 1 remainder 2 |
| 6 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 128 and 35 | 4480 |
| 191 and 116 | 22156 |
| 64 and 89 | 5696 |
| 113 and 95 | 10735 |
| 122 and 170 | 10370 |