Least Common Multiple (LCM) of 145 and 196
The least common multiple (LCM) of 145 and 196 is 28420.
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 196?
First, calculate the GCD of 145 and 196 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 145 ÷ 196 = 0 remainder 145 |
| 2 | 196 ÷ 145 = 1 remainder 51 |
| 3 | 145 ÷ 51 = 2 remainder 43 |
| 4 | 51 ÷ 43 = 1 remainder 8 |
| 5 | 43 ÷ 8 = 5 remainder 3 |
| 6 | 8 ÷ 3 = 2 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 35 and 50 | 350 |
| 183 and 159 | 9699 |
| 46 and 119 | 5474 |
| 105 and 83 | 8715 |
| 134 and 160 | 10720 |