Least Common Multiple (LCM) of 145 and 91
The least common multiple (LCM) of 145 and 91 is 13195.
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 145 and 91?
First, calculate the GCD of 145 and 91 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 91 = 1 remainder 54 |
| 2 | 91 ÷ 54 = 1 remainder 37 |
| 3 | 54 ÷ 37 = 1 remainder 17 |
| 4 | 37 ÷ 17 = 2 remainder 3 |
| 5 | 17 ÷ 3 = 5 remainder 2 |
| 6 | 3 ÷ 2 = 1 remainder 1 |
| 7 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 172 and 97 | 16684 |
| 199 and 92 | 18308 |
| 120 and 70 | 840 |
| 144 and 141 | 6768 |
| 172 and 149 | 25628 |