Question

The numbers 176 and 342,written as the products of their prime factors,are 176=2x2x2x2x11 and 342=2x3x3x19. Hence,find the smallest whole number that is divisible by both 176 and 342

Answer 1

176=2*2*2*2*11

342=2*3*3*19

To find smallest whole number we need to find LCM (lowest common factor)

Hence,LCM of 176 and 342 is

2*2*2*2*3*3*11*19=30096

Answer 2

Answer:

 The smallest number that is divisible by both 176 and 342 is 30096.

Step-by-step explanation:

Least common multiple:

• The least common multiple of two or more numbers is the number that can be divisible by both the numbers.

• The least common multiple is abbreviated as L.C.M.

Types to find L.C.M:

• Listing the multiples: In this method we list all the multiples and then take the common multiple as the L.C.M.
• Prime factorization: IN this method we write all the multiples in the form of prime factors and take all the common multiples and also the single multiple and then the product of all multiples gives L.C.M.

       Given

            176 = 2x2x2x2x11

           342 = 2x3x3x19

   To find the smallest number that is divisible by both 176 and 342.

   We need to find LCM of 176 and 342.

      The common multiples of 176 and 342 are

         L.C.M = 2x2x2x2x3x11x19

                    = 30096

    Hence, the smallest number that is divisible by both 176 and 342 is 30096.

Know more about Factorization:

https://brainly.in/question/6388449?referrer=searchResults