Free LCM Calculator determines the least common multiple (LCM) between 32 and 48 the smallest integer that is 96 that is divisible by both numbers.

Least Common Multiple (LCM) of 32 and 48 is **96**.

LCM(32,48) = 96

*Least common multiple* or lowest common denominator (LCD) can be calculated in three ways;

- Least Common Multiple of 32 and 48 by Prime method
- Least Common Multiple of 32 and 48 with GCF Formula

Least common multiple can be found by multiplying the highest exponent prime factors of 32 and 48. First we will calculate the **prime factors of 32 and 48**.

**Prime Factorization of 32**

2 | 32 |

2 | 16 |

2 | 8 |

2 | 4 |

2 | 2 |

1 |

Prime factors of 32 are 2. Prime factorization of **32** in exponential form is:

32 = 2^{5}

**Prime Factorization of 48**

2 | 48 |

2 | 24 |

2 | 12 |

2 | 6 |

3 | 3 |

1 |

Prime factors of 48 are 2,3. Prime factorization of **48** in exponential form is:

48 = 2^{4}×3^{1}

Now multiplying the highest exponent prime factors to calculate the **LCM of 32 and 48**.

LCM(32,48) = 2^{5}×3^{1}

LCM(32,48) = 96

**Factors of 32**

List of positive integer factors of 32 that divides 32 without a remainder.

1, 2, 4, 8, 16, 32

**Factors of 48**

List of positive integer factors of 48 that divides 48 without a remainder.

1, 2, 3, 4, 6, 8, 12, 16, 24, 48

The formula of **LCM** is LCM(a,b) = ( a × b) / GCF(a,b).

We need to calculate greatest common factor 32 and 48, than apply into the LCM equation.

GCF(32,48) = 16

LCM(32,48) = ( 32 × 48) / 16

LCM(32,48) = 1536 / 16

LCM(32,48) = 96

(i) The LCM of 48 and 32 is associative

LCM of 32 and 48 = LCM of 48 and 32

1. What is the LCM of 32 and 48?

Answer: LCM of 32 and 48 is 96.

2. What are the Factors of 32?

Answer: Factors of 32 are 1, 2, 4, 8, 16, 32. There are 6 integers that are factors of 32. The greatest factor of 32 is 32.

3. What are the Factors of 48?

Answer: Factors of 48 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 48. There are 10 integers that are factors of 48. The greatest factor of 48 is 48.

4. How to Find the LCM of 32 and 48?

Answer:

Least Common Multiple of 32 and 48 = 96

Step 1: Find the prime factorization of 32

32 = 2 x 2 x 2 x 2 x 2

Step 2: Find the prime factorization of 48

48 = 2 x 2 x 2 x 2 x 3

Step 3: Multiply each factor the greater number of times it occurs in steps i) or ii) above to find the lcm:

LCM = 96 = 2 x 2 x 2 x 2 x 2 x 3

Step 4: Therefore, the least common multiple of 32 and 48 is 96.