Lcm for 2/3,4/9,8/15 numbers

lcd = 3*3*5 = 45

8/45

To find the Least Common Multiple (LCM) of the fractions 2/3, 4/9, and 8/15, we need to find the LCM of their denominators first.

Step 1: Find the LCM of the denominators (3, 9, and 15).

To find the LCM, we can list the multiples of each number and find the smallest common multiple:

Multiples of 3: 3, 6, 9, 12, 15, 18, 21, 24, ...

Multiples of 9: 9, 18, 27, 36, 45, 54, 63, 72, ...

Multiples of 15: 15, 30, 45, 60, 75, 90, ...

From these lists, we can see that the smallest common multiple is 45.

Step 2: Convert the fractions to have a common denominator of 45.

To convert the fractions to have the common denominator 45, we multiply the numerator and denominator of each fraction by the appropriate factor.

For 2/3: Multiply both the numerator and denominator by 15 (to get a denominator of 45): (2 * 15) / (3 * 15) = 30/45

For 4/9: Multiply both the numerator and denominator by 5 (to get a denominator of 45): (4 * 5) / (9 * 5) = 20/45

For 8/15: The fraction already has a denominator of 15, so we do not need to convert.

Step 3: Find the LCM of the numerators.

Now that we have the fractions with a common denominator of 45, we can find the LCM of the numerators (30, 20, and 8).

To find the LCM of the numerators, we can list the multiples of each number and find the smallest common multiple:

Multiples of 30: 30, 60, 90, 120, ...

Multiples of 20: 20, 40, 60, 80, ...

Multiples of 8: 8, 16, 24, 32, 40, 48, ...

From these lists, we can see that the LCM of the numerators is 120.

Therefore, the LCM of the fractions 2/3, 4/9, and 8/15 is 120/45.