Least Common Multiple (LCM) of 91 and 143
The least common multiple (LCM) of 91 and 143 is 1001.
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 91 and 143?
First, calculate the GCD of 91 and 143 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 91 ÷ 143 = 0 remainder 91 |
| 2 | 143 ÷ 91 = 1 remainder 52 |
| 3 | 91 ÷ 52 = 1 remainder 39 |
| 4 | 52 ÷ 39 = 1 remainder 13 |
| 5 | 39 ÷ 13 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 178 | 9078 |
| 69 and 155 | 10695 |
| 188 and 115 | 21620 |
| 12 and 172 | 516 |
| 112 and 135 | 15120 |