To find the highest common factor (HCF) and lowest common multiple (LCM) of two numbers, we can use their prime factors.
.png "What is the HCF and LCM of 12 and 15?")
The prime factorization of 12 is 2 × 2 × 3.
The prime factorization of 15 is 3 × 5.
To find the HCF, we need to find the highest common factor of these two sets of factors. The only factor they have in common is 3.
Therefore, the HCF of 12 and 15 is 3.
To find the LCM, we need to find the lowest multiple that both 12 and 15 have in common. We can start by listing the multiples of 12 and 15 until we find the smallest one they have in common.
To find the LCM, we need to find the lowest multiple that both 12 and 15 have in common. We can start by listing the multiples of 12 and 15 until we find the smallest one they have in common.
Multiples of 12: 12, 24, 36, 48, 60, 72, 84, 96, 108, 120, ..
Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, ...
We can see that 60 is the smallest multiple that both 12 and 15 have in common.
Therefore, the LCM of 12 and 15 is 60.
So, the HCF of 12 and 15 is 3, and the LCM of 12 and 15 is 60.
To find the LCM of 12 and 15 using the prime factorization method, we need to find the prime factors of both numbers and then multiply the highest power of each prime factor.
So, the HCF of 12 and 15 is 3, and the LCM of 12 and 15 is 60.
What is the LCM of 12 and 15 using the prime factorization method?
To find the LCM of 12 and 15 using the prime factorization method, we need to find the prime factors of both numbers and then multiply the highest power of each prime factor.
The prime factorization of 12 is 2 × 2 × 3.
The prime factorization of 15 is 3 × 5.
To find the LCM, we need to find the highest power of each prime factor that appears in either factorization.
The highest power of 2 that appears in the factorization of 12 is 2 × 2 = 4.
The highest power of 2 that appears in the factorization of 15 is 2^0 = 1.
Therefore, we need to multiply by 2^2 = 4.
The highest power of 3 that appears in the factorization of 12 is 3^1 = 3.
The highest power of 3 that appears in the factorization of 12 is 3^1 = 3.
The highest power of 3 that appears in the factorization of 15 is 3^1 = 3.
Therefore, we need to multiply by 3^1 = 3.
The highest power of 5 that appears in the factorization of 12 is 5^0 = 1.
The highest power of 5 that appears in the factorization of 12 is 5^0 = 1.
The highest power of 5 that appears in the factorization of 15 is 5^1 = 5.
Therefore, we need to multiply by 5^1 = 5.
Multiplying these highest powers of each prime factor together gives us the LCM of 12 and 15:
Multiplying these highest powers of each prime factor together gives us the LCM of 12 and 15:
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