Question

The LCM of two numbers is 7 times their HCF. The sum of LCM and HCF is 240. find
the two numbers.​

Answer 1

Answer:

Step-by-step explanation:

Let the two numbers be a and b

L.C.M of a and b is 7 times H.C.F of a and b

⇒ L.C.M = 7 x H.C.F → equation 1

The sum of L.C.M and H.C.F =240

⇒ L.C.M + H.C.F = 240 → equation 2

Substituting equation 1 in equation 2

equation 2 ⇒ 7 H.C.F + H.C.F = 240

⇒ 8 H.C.F = 240

⇒ H.C.F = 240 / 8

⇒ H.C.F = 30

Substituting H.C.F = 30 in equation 1

equation 1 ⇒ L.C.M = 7 x H.C.F

⇒ L.C.M = 7 x 30

⇒ L.C.M = 210

We know that product of 2 numbers = Their H.C.F x L.C.M

⇒ a x b = 30 x 210

⇒ ax b = 6300

Answer 2

Answer:

a = 210 and b = 30

Step-by-step explanation:

l.c.m(a,b) = 7(h.c.f(a,b))

l.c.m(a,b) = 7(h.c.f(a,b))let. h.c.f(a,b). be x

l.c.m(a,b) = 7(h.c.f(a,b))let. h.c.f(a,b). be xl.c.m(a,b). = 7x

l.c.m(a,b) = 7(h.c.f(a,b))let. h.c.f(a,b). be xl.c.m(a,b). = 7x:: l.c.m(a,b) + h.c.f(a,b) = 240

l.c.m(a,b) = 7(h.c.f(a,b))let. h.c.f(a,b). be xl.c.m(a,b). = 7x:: l.c.m(a,b) + h.c.f(a,b) = 2407x+x = 240

l.c.m(a,b) = 7(h.c.f(a,b))let. h.c.f(a,b). be xl.c.m(a,b). = 7x:: l.c.m(a,b) + h.c.f(a,b) = 2407x+x = 240x = 30

l.c.m(a,b) = 7(h.c.f(a,b))let. h.c.f(a,b). be xl.c.m(a,b). = 7x:: l.c.m(a,b) + h.c.f(a,b) = 2407x+x = 240x = 30::h.c.f(a,b)=30

l.c.m(a,b) = 7(h.c.f(a,b))let. h.c.f(a,b). be xl.c.m(a,b). = 7x:: l.c.m(a,b) + h.c.f(a,b) = 2407x+x = 240x = 30::h.c.f(a,b)=30l.c.m(a,b) =7x30

l.c.m(a,b) = 7(h.c.f(a,b))let. h.c.f(a,b). be xl.c.m(a,b). = 7x:: l.c.m(a,b) + h.c.f(a,b) = 2407x+x = 240x = 30::h.c.f(a,b)=30l.c.m(a,b) =7x30 =210

l.c.m(a,b) = 7(h.c.f(a,b))let. h.c.f(a,b). be xl.c.m(a,b). = 7x:: l.c.m(a,b) + h.c.f(a,b) = 2407x+x = 240x = 30::h.c.f(a,b)=30l.c.m(a,b) =7x30 =210

l.c.m(a,b) = 7(h.c.f(a,b))let. h.c.f(a,b). be xl.c.m(a,b). = 7x:: l.c.m(a,b) + h.c.f(a,b) = 2407x+x = 240x = 30::h.c.f(a,b)=30l.c.m(a,b) =7x30 =210 l.c.m(a,b) x h.c.f(a,b) = a x b

l.c.m(a,b) = 7(h.c.f(a,b))let. h.c.f(a,b). be xl.c.m(a,b). = 7x:: l.c.m(a,b) + h.c.f(a,b) = 2407x+x = 240x = 30::h.c.f(a,b)=30l.c.m(a,b) =7x30 =210 l.c.m(a,b) x h.c.f(a,b) = a x b210 x 30 = a x b

l.c.m(a,b) = 7(h.c.f(a,b))let. h.c.f(a,b). be xl.c.m(a,b). = 7x:: l.c.m(a,b) + h.c.f(a,b) = 2407x+x = 240x = 30::h.c.f(a,b)=30l.c.m(a,b) =7x30 =210 l.c.m(a,b) x h.c.f(a,b) = a x b210 x 30 = a x b:::; on comparing we get,

l.c.m(a,b) = 7(h.c.f(a,b))let. h.c.f(a,b). be xl.c.m(a,b). = 7x:: l.c.m(a,b) + h.c.f(a,b) = 2407x+x = 240x = 30::h.c.f(a,b)=30l.c.m(a,b) =7x30 =210 l.c.m(a,b) x h.c.f(a,b) = a x b210 x 30 = a x b:::; on comparing we get, a = 210 and b = 30