Question

Finthe Hcf and lcm of a and b for the numbers a=2⁵×3⁷×5²×7 and b= 2³×3²×5⁶×11 . Also check if hcf (a,b) × lcm (a,b) = a×b

Answer 1

Step-by-step explanation:

Given that:

Find the HCF and LCM of a and b for the numbers a=2⁵×3⁷×5²×7

and b= 2³×3²×5⁶×11 . Also check if hcf (a,b) × lcm (a,b) = a×b

To find: HCF and LCM

Solution:

HCF:

$a= {2}^{5} \times {3}^{7} \times {5}^{2} \times 7 \\ b = {2}^{3} \times {3}^{2} \times {5}^{6} \times 11 \\ \\ H.C.F(a,b) = {2}^{3} \times {3}^{2} \times {5}^{2} \\ \\ H.C.F(a,b) = 8 \times 9 \times 25 \\ \\ H.C.F(a,b) = 72 \times 25 \\ \\ \bold{H.C.F(a,b) =1800}$

LCM:

$a= {2}^{5} \times {3}^{7} \times {5}^{2} \times 7 \\ b = {2}^{3} \times {3}^{2} \times {5}^{6} \times 11 \\ \\ L.C.M(a,b) = {2}^{5} \times {3}^{7} \times {5}^{6} \times 7 \times 11 \\ \\ L.C.M(a,b)= 32 \times 2187 \times 15625 \times 77 \\ \\ \bold{L.C.M(a,b) = 84199500000}$

To check: Whether hcf (a,b) × lcm (a,b) = a×b

$H.C.F(a,b) \times L.C.M(a,b) = 1800 \times 84199500000 \\ \\ \bold{H.C.F(a,b) \times L.C.M(a,b) = 151559100000000 }\: \: \:... eq1 \\ \\ a \times b = {2}^{8} \times {3}^{9} \times {5}^{8} \times 7 \times 11 \\ \\ a \times b = 256 \times 19683 \times 390625 \times 77 \\ \\ \bold{a\times\:b = 151559100000000} \: \: \: ...eq2$

From eq1 and eq2,

it is proved that HCF(a,b) × LCM (a,b) = a×b

Hope it helps you.

Answer 2

Answer:

H.C.F= 1800

L.C.M=84199500000