Least Common Multiple (LCM) of 46 and 174
The least common multiple (LCM) of 46 and 174 is 4002.
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 46 and 174?
First, calculate the GCD of 46 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 46 ÷ 174 = 0 remainder 46 |
| 2 | 174 ÷ 46 = 3 remainder 36 |
| 3 | 46 ÷ 36 = 1 remainder 10 |
| 4 | 36 ÷ 10 = 3 remainder 6 |
| 5 | 10 ÷ 6 = 1 remainder 4 |
| 6 | 6 ÷ 4 = 1 remainder 2 |
| 7 | 4 ÷ 2 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 24 and 68 | 408 |
| 115 and 113 | 12995 |
| 74 and 173 | 12802 |
| 16 and 123 | 1968 |
| 55 and 198 | 990 |