Question

The greatest 3-digit number which is a multiple of both 50 and 70 is

Answer 1

Answer:

700 is the correct answer :)

Answer 2

Answer:

The lcm of 70 and 50 can be obtained like this:

• The multiples of 70 are … , 280, 350, 420,..
• The multiples of 50 are …, 300, 350, 400, …
• The common multiples of 70 and 50 are n x 350, intersecting the two sets above, n≠0 ∈ Z.
• In the intersection multiples of 70 ∩ multiples of 50 the least positive element is 350.
• Therefore, the least common multiple of 70 and 50 is 350.

(or)

$lcm(70,50) = \frac{70 \times 50}{gcf(70,50)}$

$= \frac{3500}{10} \\= 350$

Alternatively, the lcm of 70 and 50 can be found using the prime factorization of 70 and 50:

• The prime factorization of 70 is: 2 x 5 x 7
• The prime factorization of 50 is: 2 x 5 x 5
• Eliminate the duplicate factors of the two lists, then multiply them once with the remaining factors of the lists to get lcm(70,70) = 350