Least Common Multiple (LCM) of 103 and 153
The least common multiple (LCM) of 103 and 153 is 15759.
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 103 and 153?
First, calculate the GCD of 103 and 153 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 153 = 0 remainder 103 |
| 2 | 153 ÷ 103 = 1 remainder 50 |
| 3 | 103 ÷ 50 = 2 remainder 3 |
| 4 | 50 ÷ 3 = 16 remainder 2 |
| 5 | 3 ÷ 2 = 1 remainder 1 |
| 6 | 2 ÷ 1 = 2 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 140 and 116 | 4060 |
| 34 and 67 | 2278 |
| 128 and 54 | 3456 |
| 16 and 17 | 272 |
| 115 and 68 | 7820 |