Minty sweets are sold in packets of 40
Lemon sweets are sold in packets of 56.
Andy wants to buy the same numbers of Minty sweets and lemon sweets.
What is the smallest number of packets of each type of sweets he could
buy?
The trial and error way--not very mathy.
56 x what number ends in a 0.
56 x 1 = no
56 x 2 = no
56 x 3 = no
56 x 4 = no
56 x 5 = 280 and 280/40 = 7
5 packets of 56 = 280 lemon sweets
7 packets of 40 = 280 minty sweets
GCD(40,56) = 8
40/8 = 5
56/8 = 7
To find the smallest number of packets of each type of sweets that Andy could buy, we need to find the least common multiple (LCM) of 40 and 56.
Step 1: Prime factorize the numbers:
40 = 2^3 * 5
56 = 2^3 * 7
Step 2: Identify the highest power of each prime factor:
The highest power of 2 is 3.
The highest power of 5 is 1.
The highest power of 7 is 1.
Step 3: Multiply the highest powers of each prime factor:
2^3 * 5^1 * 7^1 = 280
Therefore, Andy could buy packets of 280 Minty sweets and 280 Lemon sweets to have an equal number of each type of sweet with the smallest number of packets.
To find the smallest number of packets of Minty and lemon sweets that Andy could buy, we need to find the smallest common multiple of 40 and 56.
First, let's find the prime factorization of 40 and 56:
40 = 2^3 * 5
56 = 2^3 * 7
Next, we look for the highest power of each prime number that appears in either factorization:
The highest power of 2 is 3.
The highest power of 5 is 1.
The highest power of 7 is 1.
To find the smallest common multiple, we multiply these prime factors together:
2^3 * 5^1 * 7^1 = 8 * 5 * 7 = 280
Therefore, Andy would need to buy 280 packets of both Minty and lemon sweets to have the same number of each type.