Least Common Multiple (LCM) of 120 and 153
The least common multiple (LCM) of 120 and 153 is 6120.
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 120 and 153?
First, calculate the GCD of 120 and 153 using the Euclidean algorithm. Then use the formula above to find the LCM.
Step-by-Step GCD Calculation
| Step | Calculation |
|---|---|
| 1 | 120 ÷ 153 = 0 remainder 120 |
| 2 | 153 ÷ 120 = 1 remainder 33 |
| 3 | 120 ÷ 33 = 3 remainder 21 |
| 4 | 33 ÷ 21 = 1 remainder 12 |
| 5 | 21 ÷ 12 = 1 remainder 9 |
| 6 | 12 ÷ 9 = 1 remainder 3 |
| 7 | 9 ÷ 3 = 3 remainder 0 |
Examples of LCM Calculations
| Numbers | LCM |
|---|---|
| 133 and 45 | 5985 |
| 37 and 31 | 1147 |
| 80 and 13 | 1040 |
| 25 and 40 | 200 |
| 141 and 119 | 16779 |