Find the LCM and HCF of the following integers by the prime factorization method.(i) 12, 15 and 21 (ii) 17, 23, and 29 (iii) 8, 9 and 25(iv) 72 and 108 (v) 306 and 657
Answers
1)
Facors of 12 = 2 x 2 x 3
Factors of 15 = 3 x 5
Factors of 21 = 3 x 7
LCM = 2 x 2 x 3 x 5 x 7 = 420
HCF = 3
2)
Facors of 17 = 17
Factors of 23 = 23
Factors of 29 = 29
LCM = 17 x 23 x 29 = 11339
HCF = Nothing
3)
Facors of 8 = 2 x 2 x 2
Factors of 9 = 3 x 3
Factors of 25 = 5 x 5
LCM = 2 x 2 x 2 x 3 x 3 x 5 x 5
HCF = Nothing
4)
Facors of 72 = 2 x 2 x 2 x 3 x 3
Factors of 108 = 2 x 2 x 3 x 3 x 3
LCM = 2 x 2 x 2 x 3 x 3 x 3 = 1458
HCF = 2 x 2 x 3 x 3 = 24
5)
Facors of 306 = 2 x 3 x 3 x 17
Factors of 657 = 3 x 3 x 73
LCM = 2 x 3 x 3 x 17 x 73 = 22338
HCF = 3 x 3 = 9
Answer:Let the lengths and breadth of rectangle be l & b respectively.
Now l = b+5, perimeter = 2(l+b) = 58 cm
2(b +b +5) = 58
2b + 5 = 29
2b = 24
b = 12 and length = b +5 = 17
Step-by-step explanation:Let the lengths and breadth of rectangle be l & b respectively.
NowLet the lengths and breadth of rectangle be l & b respectively.
Now l = b+5, perimeter = 2(l+b) = 58 cm
2(b +b +5) = 58
2b + 5 = 29
2b = 24
b = 12 and length = b +5 = 17
l = b+5, perimeter = 2(l+b) = 58 cm
2(b +b +5) = 58
2b + 5 = 29
2b = 24
b = 12 and length = b +5 = 17