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What is the least common multiple of 2 and 4?

The main objective of this question is to find the least common multiple.

This question uses the concept of least common multiple. The least common multiple, also known as the lowest common multiple of two integers x and y, and typically denoted by the notation lcm(x, y). This is indeed the lowest positive integer which is divisible both by x and y. This concept is used in the fields of arithmetic and number theory.

Expert Answer

We have to find the least common multiple for $ 2 $ and $ 4 $.

First, we will find the factorization of $ 2 $, which is:

\[ \space 2 \space = \space 2 \]

Now the factorization of 4 is:

\[ \space 2^2 \space = \space 2 \space \times \space 2 \space = \space 4 \]

Thus the least common factor is $ 4 $.

Numerical Answer

The least common factor for $ 2 $ and $ 4 $ is $ 4 $.

Example

Find the least common multiple for:

  • \[ \space 3 \space and \space 9 \]
  • \[ \space 4 \space and \space 16 \]
  • \[ \space 5 \space and \space 25 \]
  • \[ \space 6 \space and \space 36 \]

We have to find the least common multiple for $ 3 $ and $ 9 $.

First, we will find the factorization of 3, which is:

\[ \space 3 \space = \space 3 \]

Now the factorization of  $ 9 $  is:

\[ \space 3^2 \space = \space 3 \space \times \space 3 \space = \space 9 \]

Thus the least common factor is $ 9 $.

Now we have to find the least common multiple for $ 4 $ and $ 16 $.

First, we will find the factorization of 4, which is:

\[ \space 2^2\space = \space 2 \space \times \space 2 \space = \space 4 \]

Now the factorization of  $ 9 $  is:

\[ \space 4^2 \space = \space 4\space \times \space 4 \space = \space 16 \]

Thus the least common factor is:

\[ \space = \space 2 \space \times \space 2 \space \times \space \times  \space 2 \space \times \space 2  \space = \space  16 \]

Now we have to find the least common multiple for $ 5 $ and $ 25 $.

First, we will find the factorization of 5, which is:

\[ \space 5\space = \space 5 \]

Now the factorization of  $ 25 $  is:

\[ \space 5^2 \space = \space 5\space \times \space 5 \space = \space 25\]

Thus the least common factor is:

\[ \space = \space 5 \space \times \space 5 \space  = \space  25 \]

Now we have to find the least common multiple for $ 6 $ and $ 36 $.

First, we will find the factorization of 6, which is:

\[ \space 6 \space = \space 2 \space \times \space 3 \space = \space 6  \]

Now the factorization of $ 36 $ is:

\[ \space 6^2 \space = \space 2\space \times \space 3 \space  \times \space  2\space \times \space 3 \space= \space 36 \]

Thus the least common factor is $ 36 $.

5/5 - (9 votes)