Least Common Multiple (LCM) of 153 and 53
The least common multiple (LCM) of 153 and 53 is 8109.
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 153 and 53?
First, calculate the GCD of 153 and 53 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 153 ÷ 53 = 2 remainder 47 |
| 2 | 53 ÷ 47 = 1 remainder 6 |
| 3 | 47 ÷ 6 = 7 remainder 5 |
| 4 | 6 ÷ 5 = 1 remainder 1 |
| 5 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 194 and 173 | 33562 |
| 71 and 120 | 8520 |
| 85 and 127 | 10795 |
| 132 and 54 | 1188 |
| 112 and 155 | 17360 |