Least Common Multiple (LCM) of 101 and 143
The least common multiple (LCM) of 101 and 143 is 14443.
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 101 and 143?
First, calculate the GCD of 101 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 101 ÷ 143 = 0 remainder 101 |
| 2 | 143 ÷ 101 = 1 remainder 42 |
| 3 | 101 ÷ 42 = 2 remainder 17 |
| 4 | 42 ÷ 17 = 2 remainder 8 |
| 5 | 17 ÷ 8 = 2 remainder 1 |
| 6 | 8 ÷ 1 = 8 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 38 and 113 | 4294 |
| 74 and 135 | 9990 |
| 120 and 171 | 6840 |
| 33 and 81 | 891 |
| 161 and 105 | 2415 |