Previously we have discussed about rational expressions applications and now we are going to study about LCM and GCF which stand for least common multiple and greatest common factor respectively. In icse text books of Grade V, we are going to study about LCM and GCF.
If we have two numbers and need to find LCM of the given numbers, then we first write the factors of the two numbers and then find the product of all the factors. We should remember that the factor occurring in both the list should be written only once. Let us use an example to make it clearer:
Find the LCM of 10 and 15.
First write the numbers as the product of prime factors separately.
10 = 1 * 2 * 5
15 = 1 * 3 * 5
5 and 1 appear in both set of prime factors, so they will be written only once while finding LCM.
So LCM of 10 and 15 = 1 * 5 * 2 * 3
= 30
Now to find GCF, first find the prime factorization of the numbers whose GCF is to be calculated.
Then take the factors which exist in both the lists and find their product.
Thus we will get GCF. (Know more about proportions in broad manner here,)
E.g. Find the GCF of 10 and 15.
First write the numbers as the product of prime factors separately.
10 = 1 * 2 * 5
15 = 1 * 3 * 5
5 and 1 appear in both set of prime factors.
So GCF of 10 and 15 = 1 * 5
The ratio of two quantities with same unit or same kind is the fraction of one quantity over another, we can also express in lowest term. The two terms are in proportion if we see that the lowest form of the two ratios gives the same result.
e.g. 5 :50 and 1: 10 are the two ratios, to check these ratios are in proportion, we convert 5 : 50 to lowest term by dividing both numerator and denominator by 5 and get 1: 10 . So we observe the two given ratios are in proportion.
In the next blog we will discuss the topic of Order of Operations in Grade V and if anyone want to know about predictions then they can refer to Internet and text books for understanding it more precisely.
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If we have two numbers and need to find LCM of the given numbers, then we first write the factors of the two numbers and then find the product of all the factors. We should remember that the factor occurring in both the list should be written only once. Let us use an example to make it clearer:
Find the LCM of 10 and 15.
First write the numbers as the product of prime factors separately.
10 = 1 * 2 * 5
15 = 1 * 3 * 5
5 and 1 appear in both set of prime factors, so they will be written only once while finding LCM.
So LCM of 10 and 15 = 1 * 5 * 2 * 3
= 30
Now to find GCF, first find the prime factorization of the numbers whose GCF is to be calculated.
Then take the factors which exist in both the lists and find their product.
Thus we will get GCF. (Know more about proportions in broad manner here,)
E.g. Find the GCF of 10 and 15.
First write the numbers as the product of prime factors separately.
10 = 1 * 2 * 5
15 = 1 * 3 * 5
5 and 1 appear in both set of prime factors.
So GCF of 10 and 15 = 1 * 5
The ratio of two quantities with same unit or same kind is the fraction of one quantity over another, we can also express in lowest term. The two terms are in proportion if we see that the lowest form of the two ratios gives the same result.
e.g. 5 :50 and 1: 10 are the two ratios, to check these ratios are in proportion, we convert 5 : 50 to lowest term by dividing both numerator and denominator by 5 and get 1: 10 . So we observe the two given ratios are in proportion.
In the next blog we will discuss the topic of Order of Operations in Grade V and if anyone want to know about predictions then they can refer to Internet and text books for understanding it more precisely.
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