SELECT * FROM question_mgmt as q WHERE id=5150 AND status=1 SELECT id,question_no,question,chapter FROM question_mgmt as q WHERE courseId=9 AND subId=6 AND chapterId=268 and ex_no='2' AND status=1 ORDER BY CAST(question_no AS UNSIGNED) CBSE Free NCERT Solution of 10th mathematics Real Numbers find the lcm and hcf of the following pairs of int

Question:

Find the LCM and HCF of the following pairs of integers and verify that LCM × HCF = product of the two numbers.
   (i) 26 and 91     (ii) 510 and 92     (iii) 336 and 54

Answer:

(i) 26 and 91

First we have to find the L.C.M and H.C.F of 26, 91 using fundamental theorem of arithmetic,
26 = 13 × 2
91 = 13 × 7
For L.C.M - list all the prime factors (only once) of 26, 91 with their greatest power.
L.C.M (26, 91) = 13 × 2 × 7 = 182
For H.C.F – write all the common factors (only once) with their smallest exponent.
H.C.F (26, 91) = 13
Verification :   L.C.M (26, 91) × H.C.F (26, 91) = 26 × 91
                      182 × 13 = 2366,       => 2366 = 2366
                      Hence, proved.

(ii) 510 and 92

First we have to find the L.C.M and H.C.F of 510, 92 using fundamental theorem of arithmetic,
510 = 2 × 3 × 5 × 17
92 = 2 × 2 × 23
For L.C.M - list all the prime factors (only once) of 510, 92 with their greatest power.
L.C.M (510, 92) = 2 × 2 × 3 × 5 × 17 × 23 = 23460
For H.C.F – write all the common factors (only once) with their smallest exponent.
H.C.F (510, 92) = 2
Verification :  L.C.M (510, 92) × H.C.F (510, 92) = 510 × 92
                     23460 × 2 = 46920,                 =>  46920 = 46920
                     Hence, proved.

(iii) 336 and 54

First we have to find the L.C.M and H.C.F of 336, 54 using fundamental theorem of arithmetic,
336 = 2 × 2 × 2 × 2  × 3 × 7 = 24 × 3 × 7
54 = 2 × 3 × 3 × 3 = 2 × 33
For L.C.M - list all the prime factors (only once) of 336, 54 with their greatest power.
L.C.M (336, 54) = 3024
For H.C.F – write all the common factors (only once) with their smallest exponent.
H.C.F (336, 54) = 2 × 3 = 6
Verification : L.C.M (336, 54) × H.C.F (336, 54) = 336 × 54
                     3024 × 6 = 18144                    => 18144 = 18144
                     Hence, proved.


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