Question

lcm of the numbers 2^7×3^4×7 and 2^3×3^4×11​

Answer 1

The LCM of the numbers 2 power 7 into 3 power 4 into 7 and 2 power 3 into 3 power 4 into 11 is 2 power 7 into 3 power 4 into 7 into 11.

Step-by-step explanation:

Given : The numbers 2 power 7 into 3 power 4 into 7 and 2 power 3 into 3 power 4 into 11.

To find : The LCM of the numbers ?

Solution :

The numbers are

2 power 7 into 3 power 4 into 7 i.e 2^7\times 3^4\times7

2 power 3 into 3 power 4 into 11 i.e 2^3\times 3^4\times11

The LCM is the least common multiple i.e. the common multiple in the numbers and the rest numbers.

Common multiples are 2^3\times 3^4

Rest multiples are

Answer 2

LCM of 2⁷ × 3⁴ × 7 and 2³ × 3⁴ × 11 is 2⁷ × 3⁴ × 7 × 11

Given :

The numbers 2⁷ × 3⁴ × 7 and 2³ × 3⁴ × 11

To find :

LCM of 2⁷ × 3⁴ × 7 and 2³ × 3⁴ × 11

Concept :

LCM :

For the given two or more numbers LCM is the least number which is exactly divisible by each of the given numbers

Solution :

Step 1 of 2 :

Write down the given numbers

First number = 2⁷ × 3⁴ × 7

Second number = 2³ × 3⁴ × 11

2 , 3 , 7 are the prime numbers present in the prime factorisation of first number

2 , 3 , 11 are the prime numbers present in the prime factorisation of second number

So 2 , 3 , 7 , 11 will be present in LCM of the numbers with highest exponents

From the given two numbers

Highest power of 2 = 7

Highest power of 3 = 4

Highest power of 7 = 1

Highest power of 11 = 1

Highest power of 7 = 1

Step 2 of 2 :

Find the LCM

The required LCM

= The product of highest powers of all prime factors

= 2⁷ × 3⁴ × 7 × 11

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