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36 | , | 48 | , | 72 |

225 | 150 | 65 |

a. | 72 |

225 |

b. | 36 |

65 |

c. | 144 |

5 |

d. | 288 |

5 |

Answer: c. | 144 |

5 |

Tip:

LCM of fraction = | LCM of numerators |

HCF of denominators |

Numerators = 36, 48 and 72.

72 is largest number among them. 72 is not divisible by 36 or 48

Start with table of 72.

72 x 2 = 144 = divisible by 72, 36 and 48

∴ LCM of numerators = 144

Denominators = 225, 150 and 65

We can see that they can be divided by 5.

On dividing by 5 we get 45, 30 and 13

We cannot divide further.

So, HCF = GCD = 5

LCM of fraction = | 144 |

5 |

36 | , | 48 | , | 72 |

75 | 150 | 135 |

a. | 12 |

1350 |

b. | 72 |

225 |

c. | 150 |

36 |

d. | 1350 |

36 |

Answer: a. | 12 |

1350 |

Tip:

LCM of fraction = | LCM of numerators |

HCF of denominators |

Numerators = 36, 48 and 72.

We can see that they can be divided by 12.

On dividing by 12 we get 3, 4 and 6.

We cannot divide further.

∴ HCF = GCD of numerators = 12

150 is largest number among them. 75 can divide 150, so neglect 75

Let's find LCM of 150 and 135

----------------------------------

5 150 135

----------------------------------

3 30 27

3 10 9

10 3

----------------------------------

HCF of fraction = | 12 |

1350 |

Find the largest number to divide all the three numbers leaving the remainders 4, 3, and 15 respectively at the end?

a. 13

b. 17

c. 78

d. 89

**Answer:** a. 13

**Explanation:**

Here greatest number that can divide means the HCF

Remainders are different so simply subtract remainders from numbers

17 - 4 = 13; 42 - 3 = 39; 93 - 15 = 78

Now let's find HCF of 13, 39 and 78

By direct observation we can see that all numbers are divisible by 13.

**∴ HCF = 13 = required greatest number**

a. 187

b. 713

c. 720

d. 727

**Answer:** b. 713

**Explanation:**

Here least number is needed that means we need the Least Common Multiple i.e. LCM

We must now first find LCM of 20, 36 and 48

-----------------------------------------

4 20 36 48

-----------------------------------------

3 5 9 12

5 3 4

-----------------------------------------

**∴ LCM = 4 x 3 x 5 x 3 x 4 = 720**

But this is not the answer because there are remainders as per the given condition.

If we observe closely, the difference between the given numbers and remainders is same

20 - 13 = 7; 48 - 1 = 7; 36 - 29 = 7

Difference is same = 7

So simply subtract this difference from LCM.

**Number = 720 - 7 = 713**

a. 36

b. 133

c. 144

d. 155

**Answer:** d. 155

**Explanation:**

Here smallest (least) number is needed that means we need the LCM

We must first find LCM of 36, 24 and 16

--------------------------------------

4 16 24 36

--------------------------------------

3 4 6 9

2 4 2 3

2 1 3

--------------------------------------

**∴ LCM = 4 x 3 x 2 x 2 x 1 x 3 = 144**

Since remainder is same just add it to this LCM

**Number = 144 + 11 = 155**