Least Common Multiple (LCM) of 152 and 113
The least common multiple (LCM) of 152 and 113 is 17176.
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 152 and 113?
First, calculate the GCD of 152 and 113 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 152 ÷ 113 = 1 remainder 39 |
| 2 | 113 ÷ 39 = 2 remainder 35 |
| 3 | 39 ÷ 35 = 1 remainder 4 |
| 4 | 35 ÷ 4 = 8 remainder 3 |
| 5 | 4 ÷ 3 = 1 remainder 1 |
| 6 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 169 and 168 | 28392 |
| 191 and 185 | 35335 |
| 29 and 31 | 899 |
| 80 and 142 | 5680 |
| 103 and 66 | 6798 |