Least Common Multiple (LCM) of 49 and 143
The least common multiple (LCM) of 49 and 143 is 7007.
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 49 and 143?
First, calculate the GCD of 49 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 49 ÷ 143 = 0 remainder 49 |
| 2 | 143 ÷ 49 = 2 remainder 45 |
| 3 | 49 ÷ 45 = 1 remainder 4 |
| 4 | 45 ÷ 4 = 11 remainder 1 |
| 5 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 88 and 89 | 7832 |
| 189 and 52 | 9828 |
| 69 and 106 | 7314 |
| 133 and 121 | 16093 |
| 126 and 63 | 126 |