Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
6.8k views
in Numbers by (15.8k points)
closed by

Find the LCM of each set of numbers using prime factorisation method.

(i) 6, 9

(ii) 8, 12

(iii) 10, 15

(iv) 14, 42

(v) 30, 40, 60

(vi) 15, 25, 75

1 Answer

+1 vote
by (44.5k points)
selected by
 
Best answer

(i) 6, 9

Prime factorisation of 6 = 2 × 3

Prime factorisation of 9 = 3 × 3

Product of common factors = 3

Product of other factors = 2 × 3 = 6

LCM (6, 9) = 3 × 6 = 18

(ii) 8, 12

8 = 2 × 4 = 2 × 2 × 2

12 = 2 × 6 = 2 × 2 × 3

Product of common factors = 2 × 2 = 4

Product of other factors = 2 × 3 = 6

LCM = Product of common factors × Product of

other factors = 4 × 6 = 24

LCM (8, 12) = 24.

(iii) 10, 15

10 = 2 × 5

15 = 3 × 5

Product of common factors = 5

Product of other factors = 2 × 3 = 6

LCM (10, 15) = Product of common factors ×

Product of other factors = 5 × 6 = 30

(iv) 14, 42

14 = 2 × 7

42 = 2 × 21 = 2 × 3 × 7

Product of common factors = 2 × 7

Product of other factor = 3

LCM (14, 42) = Product of common factors ×

Product of other factors = 2 × 7 × 3 = 42

LCM (14, 42) = 42

(v) 30, 40, 60

30 = 3 × 2 × 5

40 = 2 × 2 × 2 × 5

60 = 2 × 3 × 2 × 5

Product of highest powers of the common factors = 3 × 23 × 5 = 120

LCM (30, 40, 60) = 120

(vi) 15, 25, 75

15 = 5 × 3

25 = 5 × 5

75 = 5 × 5 × 3

Product of the highest powers of the common factors = 3 × 52 = 3 × 25 = 75

LCM (15, 25, 75) = 75

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...