Ex. 1. Find the H.C.F. of 2² x 3² x 5 x 7⁴, 2² x 3⁵ x 7³, 2² x 5³ x 7².
Sol.
The prime numbers common to given numbers are 2, 5 and 7.
H.C.F. =2² x 5 x 7²= 980.
Ex.2. find the H.C.F. of 108, 288 and 360.
Sol.
108=2² x 3², 288= 2⁵ x 3² and 360 = 2² x 5 x 3²
H.C.L.= 2² x 3² =36.
Ex.3. reduce 391/667 to lowest terms.
Sol.
H.C.F. of dividing the numerator and denominator by 23, we get:
391/667 = 391/23 667/23 =17/29.
Ex.4. find the L.C.M. of 2² x 3³ x 5 x 7², 2³ x 3² x 5² x 7⁴, and 2 x 3 x 5³ x 7 x 11.
Sol.
L.C.M. = product of highest powers of 2,3,5,7 and 11= 2³ x 4³ x 5³ x 7⁴x 11.
Ex.5.find the L.C.M. of 72, 108 and 2100
Sol.
72=2² x 3², 108= 3³x 2², 2100 = 2² x 5² x 3 x 7.
L.C.M. = 2² x 3³ x 5² x 7 =37800.
Ex.6. find the H.C.F. and L.C.M. of 2/3,8/9,16/81 and 10/27.
Sol.
H.C.F. of given fractions = H.C.F. OF 2, 8, 16, 10 = 2/81.
L.C.M. OF 3, 9, 81, 27
L.C.M. Of given fractions = L.C.M. of 2, 8, 16, 10 = 80/3.
H. C.F OF 3, 9, 81, 27
Ex.7. find H.C.F. and L.C.M. of o.63. 1.05 And 2.1.
Sol.
making the same number of decimal place, the given numbers is 0.63, 1.05 and 2.10.
Without decimal, places, the given numbers are 0.63, 105 and 210.
Now, H.C.F of 63, 105 and 210 is 21.
H.C.F. of 0.63, 1.05 and 2.1 is 0.21.
L.C.M. of 63, 105 and 210 is 630.
L.C.M. Of 0.63, 1.05 and 2.1 is 6.30.
Ex. 8. Two numbers are in the ratio of 15: 11. If their H.C.F. is 13, find the numbers.
Sol.
Let the required numbers be 15 x and 11 x.
Then, their H.C.F.is X so, X = 13.
The numbers are (15 x 13 and 11 x 13) i.e., 195 and 143.
Ex. 9. The H.C.F. of two numbers is 111 and their L.C.M. is 693. If one of the numbers is 77, find the other.
Sol.
Other number = (11 x 693/77) = 99.
Ex. 10. The H.C.F. of two numbers is 11 and their L.C.M. is 693. If one of the numbers.
Sol.
other number = (11 x 693 / 77) = 99
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