Least Common Multiple (LCM) of 30 and 91
The least common multiple (LCM) of 30 and 91 is 2730.
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 30 and 91?
First, calculate the GCD of 30 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 30 ÷ 91 = 0 remainder 30 |
| 2 | 91 ÷ 30 = 3 remainder 1 |
| 3 | 30 ÷ 1 = 30 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 102 and 75 | 2550 |
| 164 and 84 | 3444 |
| 148 and 176 | 6512 |
| 119 and 17 | 119 |
| 113 and 170 | 19210 |