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Which of the following are two consecutive prime numbers that differ by 2?
Identify the numbers with only 1 as their common factor.
Find the smallest whole number that is divisible by 10 and 12.
Multiples of 10: 10, 20, 30, 40, 50, 60, 70,...
Multiples of 12: 12, 24, 36, 48, 60, 72,...
∴ The smallest whole number divisible by both 10 and 12 is 60.
Stamps in an album can be arranged as 12 per page or 18 per page exactly. What is the greatest number of stamps one can have if they are fewer than 500?
L.C.M. of 12 and 18 is 36.
∴ The required number of stamps is the largest multiple of 36, less than 500.
500 ÷ 36 = 13 R 32 as 36 × 13 = 468 and 36 × 14 = 504.
Thus, the required number of stamps = 468.
Coprime numbers have no common factor other than1, So, their L.C.M. is their product.
12 = 2 × 2 × 3
24 = 2 × 2 × 2 × 3
36 = 2 × 2 × 3 × 3
L.C.M. of 12, 24 and 36 = 2 × 2 × 3 × 2 × 3 = 72.
The prime numbers that differ by 2 are called twin primes. e.g., 3, 5 as both 3 and 5 are prime numbers and their difference is 2.
Factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18 and 36.
Factors of 144 are 1, 2, 3, 4, 6 8, 9, 12, 16, 18, 24, 36, 48, 72 and 144.
The common factors of 36 and 144 are 1, 2, 3, 4, 6, 9, 12, 18 and 36 of which 36 is the highest.
∴ H.C.F of 36 and 144 is 36.
Coprime numbers have no common factor other than 1. So, their H.C.F is 1.
______ is the least common multiple of 45 and 50. What is the value of10P + 100?
L.C.M. of 45 and 50 is 5 × 9 × 10 = 450 = P.
∴ 10P + 100 = 450 × 10 + 100 = 4500 + 100 = 4600.
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