Least Common Multiple (LCM) of 152 and 55
The least common multiple (LCM) of 152 and 55 is 8360.
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 55?
First, calculate the GCD of 152 and 55 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 152 ÷ 55 = 2 remainder 42 |
| 2 | 55 ÷ 42 = 1 remainder 13 |
| 3 | 42 ÷ 13 = 3 remainder 3 |
| 4 | 13 ÷ 3 = 4 remainder 1 |
| 5 | 3 ÷ 1 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 160 and 53 | 8480 |
| 21 and 112 | 336 |
| 20 and 100 | 100 |
| 129 and 13 | 1677 |
| 175 and 66 | 11550 |