Least Common Multiple (LCM) of 91 and 150
The least common multiple (LCM) of 91 and 150 is 13650.
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 150?
First, calculate the GCD of 91 and 150 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 91 ÷ 150 = 0 remainder 91 |
| 2 | 150 ÷ 91 = 1 remainder 59 |
| 3 | 91 ÷ 59 = 1 remainder 32 |
| 4 | 59 ÷ 32 = 1 remainder 27 |
| 5 | 32 ÷ 27 = 1 remainder 5 |
| 6 | 27 ÷ 5 = 5 remainder 2 |
| 7 | 5 ÷ 2 = 2 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 11 and 70 | 770 |
| 21 and 17 | 357 |
| 105 and 171 | 5985 |
| 175 and 175 | 175 |
| 68 and 21 | 1428 |