7. | Three number are in the ratio of 3 : 4 : 5 and their L.C.M. is 2400. Their H.C.F. is: | |||||||

Let the numbers be 3 Then, their L.C.M. = 60 So, 60 The numbers are (3 x 40), (4 x 40) and (5 x 40). Hence, required H.C.F. = 40. |

8. | The G.C.D. of 1.08, 0.36 and 0.9 is: | |||||||

Given numbers are 1.08, 0.36 and 0.90. H.C.F. of 108, 36 and 90 is 18, H.C.F. of given numbers = 0.18. |

9. | The product of two numbers is 2028 and their H.C.F. is 13. The number of such pairs is: | |||||||

Let the numbers 13 Then, 13 Now, the co-primes with product 12 are (1, 12) and (3, 4). [Note: Two integers So, the required numbers are (13 x 1, 13 x 12) and (13 x 3, 13 x 4). Clearly, there are 2 such pairs. |

10. | The least multiple of 7, which leaves a remainder of 4, when divided by 6, 9, 15 and 18 is: | |||||||

L.C.M. of 6, 9, 15 and 18 is 90. Let required number be 90 Least value of Required number = (90 x 4) + 4 = 364. |