Least Common Multiple (LCM) of 150 and 91
The least common multiple (LCM) of 150 and 91 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 150 and 91?
First, calculate the GCD of 150 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 150 ÷ 91 = 1 remainder 59 |
| 2 | 91 ÷ 59 = 1 remainder 32 |
| 3 | 59 ÷ 32 = 1 remainder 27 |
| 4 | 32 ÷ 27 = 1 remainder 5 |
| 5 | 27 ÷ 5 = 5 remainder 2 |
| 6 | 5 ÷ 2 = 2 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 21 and 150 | 1050 |
| 159 and 69 | 3657 |
| 157 and 71 | 11147 |
| 57 and 146 | 8322 |
| 130 and 45 | 1170 |