Least Common Multiple (LCM) of 61 and 143
The least common multiple (LCM) of 61 and 143 is 8723.
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 61 and 143?
First, calculate the GCD of 61 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 61 ÷ 143 = 0 remainder 61 |
| 2 | 143 ÷ 61 = 2 remainder 21 |
| 3 | 61 ÷ 21 = 2 remainder 19 |
| 4 | 21 ÷ 19 = 1 remainder 2 |
| 5 | 19 ÷ 2 = 9 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 111 and 36 | 1332 |
| 40 and 40 | 40 |
| 173 and 99 | 17127 |
| 112 and 197 | 22064 |
| 48 and 79 | 3792 |