Least Common Multiple (LCM) of 91 and 142
The least common multiple (LCM) of 91 and 142 is 12922.
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 142?
First, calculate the GCD of 91 and 142 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 91 ÷ 142 = 0 remainder 91 |
| 2 | 142 ÷ 91 = 1 remainder 51 |
| 3 | 91 ÷ 51 = 1 remainder 40 |
| 4 | 51 ÷ 40 = 1 remainder 11 |
| 5 | 40 ÷ 11 = 3 remainder 7 |
| 6 | 11 ÷ 7 = 1 remainder 4 |
| 7 | 7 ÷ 4 = 1 remainder 3 |
| 8 | 4 ÷ 3 = 1 remainder 1 |
| 9 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 15 and 23 | 345 |
| 134 and 85 | 11390 |
| 16 and 115 | 1840 |
| 170 and 105 | 3570 |
| 160 and 186 | 14880 |