Least Common Multiple (LCM) of 152 and 165
The least common multiple (LCM) of 152 and 165 is 25080.
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 165?
First, calculate the GCD of 152 and 165 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 152 ÷ 165 = 0 remainder 152 |
| 2 | 165 ÷ 152 = 1 remainder 13 |
| 3 | 152 ÷ 13 = 11 remainder 9 |
| 4 | 13 ÷ 9 = 1 remainder 4 |
| 5 | 9 ÷ 4 = 2 remainder 1 |
| 6 | 4 ÷ 1 = 4 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 141 and 196 | 27636 |
| 172 and 72 | 3096 |
| 110 and 14 | 770 |
| 62 and 176 | 5456 |
| 120 and 130 | 1560 |