Least Common Multiple (LCM) of 100 and 153
The least common multiple (LCM) of 100 and 153 is 15300.
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 100 and 153?
First, calculate the GCD of 100 and 153 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 100 ÷ 153 = 0 remainder 100 |
| 2 | 153 ÷ 100 = 1 remainder 53 |
| 3 | 100 ÷ 53 = 1 remainder 47 |
| 4 | 53 ÷ 47 = 1 remainder 6 |
| 5 | 47 ÷ 6 = 7 remainder 5 |
| 6 | 6 ÷ 5 = 1 remainder 1 |
| 7 | 5 ÷ 1 = 5 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 82 and 36 | 1476 |
| 113 and 63 | 7119 |
| 124 and 133 | 16492 |
| 180 and 71 | 12780 |
| 125 and 75 | 375 |