Least Common Multiple (LCM) of 53 and 145
The least common multiple (LCM) of 53 and 145 is 7685.
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 53 and 145?
First, calculate the GCD of 53 and 145 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 53 ÷ 145 = 0 remainder 53 |
| 2 | 145 ÷ 53 = 2 remainder 39 |
| 3 | 53 ÷ 39 = 1 remainder 14 |
| 4 | 39 ÷ 14 = 2 remainder 11 |
| 5 | 14 ÷ 11 = 1 remainder 3 |
| 6 | 11 ÷ 3 = 3 remainder 2 |
| 7 | 3 ÷ 2 = 1 remainder 1 |
| 8 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 98 and 107 | 10486 |
| 103 and 61 | 6283 |
| 105 and 21 | 105 |
| 44 and 107 | 4708 |
| 63 and 48 | 1008 |