Question

Find the lcm of 3ab 18b 9ab

Answer 1

18ab

Explanation:

The least common multiple (LCM) of two or more numbers is the smallest number that is a multiple of each of the given numbers.

To find the least common multiple (LCM) of the given expressions, we first need to factor them and then find the product of all the unique prime factors raised to their highest powers.

In this case, the expressions are:

1. 3ab

2. 18b

3. 9ab

Let's factor each expression:

1. 3ab = 3 × a × b

2. 18b = 2 × 3 × 3 × b

3. 9ab = 3 × 3 × a × b

Now, we find the LCM by taking all the unique prime factors raised to their highest powers:

The unique prime factors in these expressions are 2 and 3.

For 2, the highest power is 2¹.

For 3, the highest power is 3².

For a and b, they both appear in all the expressions at least once.

So, the LCM will be: 2¹ × 3² × a × b

LCM = 2 × 9 × ab

LCM = 18ab

So, the LCM of 3ab, 18b, and 9ab is 18ab.

Answer 2

LCM = 18ab

Explanation:

given

3ab, 18b , 9ab

the lowest common multiple (LCM) is the lowest value that the 3 given terms are factors of.

Take all the prime numbers with largest exponent from the prime factorisation.

3ab has prime factor of 3

18b has prime factors of 2 and 3²

9ab has prime factor of 3

There is only one a and one b from the variables

The maximum occurrence of 2 is 1 time

the maximum occurrence of 3 is twice , that is 3²

the maximum occurrence of a and b is 1 time

the LCM is then the product of the occurrences

LCM = 2 × 3² × a × b = 2 × 9 × a × b = 18ab