Least Common Multiple (LCM) of 105 and 91
The least common multiple (LCM) of 105 and 91 is 1365.
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 105 and 91?
First, calculate the GCD of 105 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 105 ÷ 91 = 1 remainder 14 |
| 2 | 91 ÷ 14 = 6 remainder 7 |
| 3 | 14 ÷ 7 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 178 and 16 | 1424 |
| 178 and 167 | 29726 |
| 68 and 42 | 1428 |
| 107 and 60 | 6420 |
| 12 and 27 | 108 |