Find the LCM and HCF of the following numbers and check their relationship.
(1) 15, 24 (ii) 8, 25 (iii) 12, 48 (iv) 30, 48
Answers
Solutions :-
1) 15 , 24
Prime factorization of 15 and 24
15 = 3 * 5
24 = 2 * 2 * 2 * 3
HCF = 3
LCM = 3 * 2 * 2 * 2 * 5 = 120
Verify their relationship
As we know that,
HCF * LCM = Product of two numbers
120 * 3 = 15 * 24
360 = 360 .
LHS = RHS
2) 8 , 25
Prime factorization of 8 and 25
8 = 2 * 2 * 2 * 1
25 = 5 * 5 * 1
HCF = 1
LCM = 2 * 2 * 2 * 5 * 5 = 200
Verify their relationship
As we know that,
HCF * LCM = Product of two numbers
1 * 200 = 8 * 25
200 = 200
LHS = RHS
3) 12 , 48
Prime factorization of 12 and 48
12 = 2 * 2 * 3
48 = 2 * 2 * 2 * 2 * 3
HCF = 2 * 2 * 3 = 12
LCM = 2 * 2 * 2 * 2 * 3 = 48
Verify their relationship
HCF * LCM = Product of two numbers
12 * 48 = 12 * 48
576 = 576
LHS = RHS
4) 30 , 48
Prime factorization of 30 and 48
30 = 3 * 2 * 5
48 = 2 * 2 * 2 * 3 * 2
HCF = 3 * 2 = 6
LCM = 2 * 3 * 2 * 2 * 2 * 5 = 240
Verify their relationship
LCM * HCF = Product of two numbers
6 * 240 = 30 * 48
1,440 = 1,440
LHS = RHS
Answer:
1) 15 , 24
Prime factorization of 15 and 24
15 = 3 * 5
24 = 2 * 2 * 2 * 3
HCF = 3
LCM = 3 * 2 * 2 * 2 * 5 = 120
Verify their relationship
As we know that,
HCF * LCM = Product of two numbers
120 * 3 = 15 * 24
360 = 360 .
LHS = RHS
2) 8 , 25
Prime factorization of 8 and 25
8 = 2 * 2 * 2 * 1
25 = 5 * 5 * 1
HCF = 1
LCM = 2 * 2 * 2 * 5 * 5 = 200
Verify their relationship
As we know that,
HCF * LCM = Product of two numbers
1 * 200 = 8 * 25
200 = 200
LHS = RHS
3) 12 , 48
Prime factorization of 12 and 48
12 = 2 * 2 * 3
48 = 2 * 2 * 2 * 2 * 3
HCF = 2 * 2 * 3 = 12
LCM = 2 * 2 * 2 * 2 * 3 = 48
Verify their relationship
HCF * LCM = Product of two numbers
12 * 48 = 12 * 48
576 = 576
LHS = RHS
4) 30 , 48
Prime factorization of 30 and 48
30 = 3 * 2 * 5
48 = 2 * 2 * 2 * 3 * 2
HCF = 3 * 2 = 6
LCM = 2 * 3 * 2 * 2 * 2 * 5 = 240
Verify their relationship
LCM * HCF = Product of two numbers
6 * 240 = 30 * 48
1,440 = 1,440