Least Common Multiple (LCM) of 143 and 174
The least common multiple (LCM) of 143 and 174 is 24882.
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 143 and 174?
First, calculate the GCD of 143 and 174 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 143 ÷ 174 = 0 remainder 143 |
| 2 | 174 ÷ 143 = 1 remainder 31 |
| 3 | 143 ÷ 31 = 4 remainder 19 |
| 4 | 31 ÷ 19 = 1 remainder 12 |
| 5 | 19 ÷ 12 = 1 remainder 7 |
| 6 | 12 ÷ 7 = 1 remainder 5 |
| 7 | 7 ÷ 5 = 1 remainder 2 |
| 8 | 5 ÷ 2 = 2 remainder 1 |
| 9 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 60 and 48 | 240 |
| 117 and 128 | 14976 |
| 108 and 140 | 3780 |
| 192 and 99 | 6336 |
| 76 and 105 | 7980 |