Least Common Multiple (LCM) of 103 and 152
The least common multiple (LCM) of 103 and 152 is 15656.
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 152?
First, calculate the GCD of 103 and 152 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 103 ÷ 152 = 0 remainder 103 |
| 2 | 152 ÷ 103 = 1 remainder 49 |
| 3 | 103 ÷ 49 = 2 remainder 5 |
| 4 | 49 ÷ 5 = 9 remainder 4 |
| 5 | 5 ÷ 4 = 1 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 150 and 99 | 4950 |
| 147 and 150 | 7350 |
| 91 and 41 | 3731 |
| 144 and 150 | 3600 |
| 20 and 154 | 1540 |