Least Common Multiple (LCM) of 152 and 83
The least common multiple (LCM) of 152 and 83 is 12616.
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 83?
First, calculate the GCD of 152 and 83 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 152 ÷ 83 = 1 remainder 69 |
| 2 | 83 ÷ 69 = 1 remainder 14 |
| 3 | 69 ÷ 14 = 4 remainder 13 |
| 4 | 14 ÷ 13 = 1 remainder 1 |
| 5 | 13 ÷ 1 = 13 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 142 and 32 | 2272 |
| 123 and 81 | 3321 |
| 89 and 161 | 14329 |
| 175 and 159 | 27825 |
| 120 and 167 | 20040 |